KYIV, Ukraine—Russia will extend its military drills with Belarus because of rising violence in Ukraine’s Donbas region, the government in Minsk said, as Russian President Vladimir Putin accepted a new round of talks with Kyiv amid warnings of an imminent Russian invasion.

Mr. Putin and French President Emmanuel Macron said after speaking Sunday that they agreed to continue seeking a diplomatic solution. Russia has amassed as many as 190,000 troops on Ukraine’s borders, including some 30,000 for exercises in its ally Belarus...

KYIV, Ukraine—Russia will extend its military drills with Belarus because of rising violence in Ukraine’s Donbas region, the government in Minsk said, as Russian President Vladimir Putin accepted a new round of talks with Kyiv amid warnings of an imminent Russian invasion.

Mr. Putin and French President Emmanuel Macron said after speaking Sunday that they agreed to continue seeking a diplomatic solution. Russia has amassed as many as 190,000 troops on Ukraine’s borders, including some 30,000 for exercises in its ally Belarus that were slated to end Sunday. Moscow demands that Kyiv abandon its aspirations to join NATO—the North Atlantic Treaty Organization—and give Russian proxies a major say in Ukraine’s future.

Sunday’s developments on the diplomatic front indicated that Mr. Putin could be willing to step back from the brink of war, at least in the immediate future, as he sought a face-saving end to the crisis. “Putin just started a new chapter,” said Oleksandr Danylyuk, a former Ukraine national-security adviser. “It’s a break that allows Putin to refocus, rethink and regroup before taking his next steps. The full war is unpredictable for him—you never know. It’s easy to start a war but you never know how it will end.”

Shelling across the cease-fire line in eastern Ukraine’s Donbas region intensified in recent days, with Russian-installed authorities in areas controlled by Moscow since 2014 ordering the mobilization of fighting-age men and urging the evacuation of women and children. Kyiv and its Western partners say these moves are part of a Russian propaganda campaign to justify a full-fledged military invasion of Ukraine, which President Biden has said he expects to happen within days.

Mr. Macron said that Russia, Ukraine, France and Germany will resume talks in the so-called Normandy format based on proposals presented by Kyiv in recent days. He and Mr. Putin agreed on the “necessity to favor a diplomatic solution to the crisis, and to do everything to achieve it,” according to the French account of the conversation. The French and Russian foreign ministers are slated to meet in coming days, while other consultations will take place in Paris, the French account said. German Chancellor Olaf Scholz is separately scheduled to speak to Mr. Putin on Monday, according to a German official.

A Macron aide said Mr. Putin told the French leader that Russian troops in Belarus would withdraw from the country once their military exercise is completed. The aide added that Mr. Putin said he was working on the withdrawal with Russia’s Defense Ministry.

Images released by Russia’s Defense Ministry on Saturday showed Russia test-launched ballistic and cruise missiles in what it described as strategic deterrence exercises. President Vladimir Putin oversaw the launches from a command center, according to a Kremlin pool report. Photo: Russian Defense Ministry/AFP via Getty Images The Wall Street Journal Interactive Edition

The situation remains combustible. The Russian and French leaders disagreed over who was to blame for violence in eastern Ukraine, the aide said. Mr. Putin blamed Ukrainian forces while Mr. Macron said Russian separatists were responsible, the aide said.

“We are still in a situation of high volatility, but there is still room for diplomacy,” the Macron aide said, adding that “diplomatic resources have not been exhausted.”

Mr. Macron also spoke with Ukrainian President Volodymyr Zelensky after Sunday’s talks with Mr. Putin, his second conversation with the Ukrainian leader in two days. The French leader commended Mr. Zelensky on his “composure and his determination to prevent escalation.”

The Kremlin, in a statement Sunday, blamed Mr. Zelensky for refusing to implement the so-called Minsk agreements that ended major combat in Donbas in 2015, and that—in Moscow’s interpretation—could give Russian proxies a significant say in Ukraine’s new setup, potentially halting the country’s alignment with the West.

Still, the Kremlin said Mr. Putin agreed to “intensify the search for solutions through diplomatic means,” including by holding another meeting on the Minsk accords between the four nations’ senior advisers in the Normandy format. While the first such meeting in Paris in January led to some progress, the second in Berlin earlier this month ended in failure.

Reservists took part in tactical training in Kyiv, Ukraine, on Saturday.

Photo: ANTONIO BRONIC/REUTERS

Retaining Russian forces in Belarus, a short distance from the Ukrainian capital Kyiv, gives Mr. Putin extra leverage to pressure Mr. Zelensky for painful concessions. Just hours before the exercises in Belarus were scheduled to end, Minsk said they would continue indefinitely. Belarus and Russia cited their allegations that Ukraine shelled civilian areas in Moscow-controlled areas of Donbas. Western officials have backed Kyiv’s assertion that these claims are part of an operation aimed at providing a pretext for a Russian-led attack.

Countries bordering Belarus have been “pumped with modern weaponry,” Belarus Defense Minister Viktor Khrenin said. Europe is being pushed toward war, he added, and “has begun to smell strongly of gunpowder.”

Ukrainian Defense Minister Oleksii Reznikov said the extension of Russia’s military drills in Belarus was expected.

“We ought to be ready to resist powerful pressure in the coming period. The enemy intends to destabilize Ukraine from within, to scare us and force us into capitulation. But we will stand firm,” he said.

U.S. troops loaded equipment onto vehicles in Rzeszów, Poland, on Saturday.

Photo: Czarek Sokolowski/Associated Press

Russian military analyst

Pavel Felgengauer said that the Russian troops currently in Belarus cannot stay indefinitely due to supply issues and will have to relocate to their bases at some point in the future. The presence in Belarus of units with bases in Russia’s Far East also exposes areas bordering China, a state of affairs that Mr. Felgengauer said Russia won’t want to maintain for long.

“If there will be a political decision to have a long-standing Russian army presence in Belarus, that’s a different story,” he said.

On Friday, Mr. Biden said that he expected Mr. Putin to launch a Russian invasion of Ukraine in the coming days, with targets including Kyiv. The Kremlin has been seeking a formal guarantee that NATO will never admit Ukraine and other former Soviet states as members and roll back troop deployments to the status quo in 1997, before the alliance admitted Eastern and Central European states.

On CNN’s “State of the Union,” Secretary of State Antony Blinken said that the continuation of Russian military exercises and massing of troops on the Ukraine border is part of the predicted groundwork Moscow has been laying for a Russian invasion of its smaller neighbor.

“All of this, along with the false-flag operations that we’ve seen unfold over the weekend tells us that the playbook we laid out is moving forward,” he said.

Despite the narrowing path toward a diplomatic solution to the standoff, discussions are continuing.

Mr. Blinken said he still planned to meet with his Russian counterpart, Foreign Minister Sergei Lavrov in Europe—unless Russia invades before.

“Until the tanks are actually rolling, and the planes are flying, we will use every opportunity and every minute we have to see if diplomacy can still dissuade President Putin from carrying this forward,” he said

Moscow on Sunday said more than 30,000 residents from eastern Ukraine’s Donbas area had crossed into Russia. People at a railway station in Russia’s bordering Rostov region.

Photo: Erik Romanenko/TASS/Zuma Press

Residents of a village in the Russia-controlled Donbas region inspected their house on Sunday after it was destroyed in a shelling.

Photo: anatolii stepanov/Agence France-Presse/Getty Images

Russia had repeatedly said it intends to pull the troops back once the drills are over, but intensifying fighting in eastern Ukraine this week has prompted claims from Moscow that Ukraine is readying a military offensive to retake territory from Russian-backed forces in the Donbas region. The separatists seized swaths of the country’s east in an armed conflict that started in 2014 and has continued ever since, claiming more than 14,000 lives.

On Sunday, Russia’s Federal Security Service, which controls the country’s borders, said more than 30,000 residents from the self-proclaimed Donetsk and Luhansk People’s Republics in the Donbas area had crossed to Russia’s neighboring Rostov region since the start of a mass evacuation of residents announced by authorities in the Russian-controlled areas on Friday. In Russia, the Rostov and Voronezh regions, which border Ukraine, announced states of emergency, citing the influx of people.

Vice President Kamala Harris said the U.S. and its allies would impose sweeping economic sanctions and export controls against Russia to target financial institutions, key industries and “those who aid and abet” an unprovoked invasion of Ukraine. Photo: Tobias Hase/Associated Press The Wall Street Journal Interactive Edition

Ukrainian military spokesman Dmytro Lutsyuk said on Sunday afternoon that 20 instances of artillery fire by Russian-led forces had been recorded in the space of 24 hours, and that one service member had been wounded and taken to a hospital with shrapnel wounds. Mr. Lutsyuk added that more than 860 residents of the breakaway republics had entered through a cease-fire line since Saturday.

Alongside the exercises in Belarus, Russia has also been conducting large-scale naval maneuvers on the Black and Azov seas, with warships in unprecedented numbers from Russia’s Baltic, Black Sea and Northern Fleets.

Russia previously said these naval drills would conclude Saturday night. While the warships and support vessels have collapsed their perimeter, they remain in the area.

“The exercises should have ended last night,” said Andrii Ryzhenko, a retired Ukrainian navy captain now with the Center for Defense Strategies, a Kyiv-based think tank. “But there is no sign that they are wrapping up. Particularly, our concern is landing ships.”

On Friday, six amphibious ships from Russia’s Baltic and Northern Fleets repositioned near the port of Chornomorske, on Crimea’s western cape, roughly 40 miles from the coastline of Ukraine’s southern Kherson region, according to Andrii Klymenko, a defense and maritime analyst with the Black Sea Institute of Strategic Studies, a Ukrainian think tank. Supporting the landing craft are a corvette, a missile boat, a minesweeper and rescue tugs, Mr. Klymenko said.

Steel shipments at a port in Ukraine. The drills’ impact on Ukraine’s vital commercial shipping remained limited.

Photo: Christopher Occhicone for The Wall Street Journal

Russia announced earlier this month that naval exercises near the Crimean coast would continue through March 11.

Despite limited live-fire drills broadcast on Russian state-owned television, Ukrainian analysts and former military officials said the Russian warships didn’t engage in large-scale maneuvers in the past week and remained mostly stationary. The lack of activity relative to previous Russian exercises on the Black Sea left Ukrainian officials to speculate about Russian intentions.

The drills’ impact on Ukraine’s vital commercial shipping remained limited. Last week, Russia restricted access to Ukraine’s Black Sea ports, leaving a ribbon of navigable waters between the live-fire area and the Ukrainian coastline. These shipping lanes from Odessa to the Bosporus are now open, Mr. Klymenko said.

Port operators in Odessa said commercial shipping continued uninterrupted. Only one ship, from Israeli container shipper ZIM, was known to have canceled an Odessa port call over concern for the naval exercises.

“All our ports are open for shipping,” said Yuriy Vaskov, Ukraine’s deputy minister of infrastructure, who is responsible for maritime issues. “All the vessels can safely pass to Ukrainian ports or from Ukrainian ports.”

The shipping corridor from Odessa to the Georgian ports of Batumi and Poti remains closed by Russia warships, however, Mr. Klymenko said.

—Peter Wonacott in Washington, Ann M. Simmons in Moscow and Noemie Bisserbe in Paris contributed to this article.

Write to Yaroslav Trofimov at yaroslav.trofimov@wsj.com and Brett Forrest at brett.forrest@wsj.com