KYIV, Ukraine—Seven people were killed and several injured in Russian missile strikes on the western Ukrainian city of Lviv, Ukrainian authorities said, shattering the calm in a place that had remained mostly unharmed in the war as Russia expanded its strikes across Ukraine.

Russian cruise missiles injured 11 people, including the child of a family that had fled to the safety of western Ukraine from Kharkiv, which had been under Russian assault since the early days of the conflict, said Lviv Mayor Andriy Sadovyi. Three of the missiles hit military infrastructure and one missile struck a tire-service shop, damaging nearby houses and vehicles, regional authorities said.

“These are the first civilian deaths in our city,” said Mr. Sadovyi. “We mourn the dead, but we must be as vigilant as possible.”

The strikes on Lviv came as Russian missiles and artillery hit hundreds of targets, leading to civilian deaths and destruction in several other Ukrainian cities, as Russia ramps up for an offensive to seize control over the eastern Donbas area. Ukrainian authorities reported four civilian deaths in a Russian attack in the front-line city of Kreminna, in the Luhansk region of the Donbas, and said they had lost control of the city. Shelling in Kharkiv, eastern Ukraine’s largest city, killed two civilians, the local prosecutors’ office said, with shells falling on playgrounds near residential buildings.

Ukrainian troops in the port city of Mariupol, meanwhile, continued to hold out a day after they rejected a Russian ultimatum to surrender. Russia has sought to capture the city to free up troops for its Donbas offensive and secure a land corridor from Russian-held territory in the east to the Crimean Peninsula.

The Ukrainian armed forces’ General Staff said that there were signs that Russia was beginning its new offensive in the east. Russia’s main efforts are “focused on establishing full control over the territory of Donetsk and Luhansk regions and maintaining the previously captured territory,” it said in a statement on Facebook.

Russia’s Defense Ministry said Monday that its air-based missiles struck 16 targets in Ukraine, but it didn’t mention Lviv among the locations targeted. Russian artillery units hit 315 Ukrainian assets overnight, the ministry said, and targeted Ukrainian troops in several locations with land-based missiles and airstrikes. The ministry didn’t respond to a request for comment on the Lviv strikes.

The attack on Lviv was the deadliest in the city since the start of the war. Lviv is far from the war’s front lines in eastern Ukraine and its relative safety has made it a common destination for Ukrainians fleeing eastern areas. The missile attacks were a reminder that Russia’s long-range weapons remain a threat for Ukrainians across much of the country at the same time some refugees are returning to the country. Previous Russian strikes had killed people outside the city in the Yavoriv district, but these were the first to reach the city.

“The Russians continue barbarically attacking Ukrainian cities from the air, cynically declaring to the whole world their ‘right’ to… kill Ukrainians,” Mykhailo Podolyak, an adviser to Ukrainian President Volodymyr Zelensky,

said on Twitter.

The shock wave from the strikes shattered the windows of a nearby hotel that was housing Ukrainians evacuated from other regions, Mr. Sadovyi said. About 40 cars were damaged or destroyed in the strike, he said.

A Ukrainian serviceman at the site of a missile strike in Lviv on Monday.

Photo: ROMAN BALUK/REUTERS

A civilian building after being hit by a Russian missile in Lviv on Monday.

Photo: Joe Raedle/Getty Images

Four civilians fleeing the war were also killed in a Russian attack in the eastern Ukrainian city of Kreminna, according to Serhiy Haidai, governor of the Luhansk region, bordering Russia. He said that control over Kreminna was lost and that street fights were under way.

In Kramatorsk, Ukraine, the site of an attack that killed more than 50 people at a train station earlier this month, authorities reported a missile strike that hit residential buildings and other infrastructure and disrupted electricity and gas supplies. No civilian casualties were reported.

Civilian evacuations out of cities near the front lines, including Mariupol, were canceled Monday, after Ukraine and Russia failed to agree on humanitarian corridors, Ukrainian Deputy Prime Minister Iryna Vereshchuk said in a Facebook post. Ms. Vereshchuk said Russian forces were blocking and shelling humanitarian routes. “For security reasons, a decision was made today not to open humanitarian corridors,” she said.

Mr. Zelensky has called for further peace negotiations to resolve the situation in Mariupol. Much of the city has been reduced to rubble, leaving most of the remaining residents without access to food, water and power. The last Ukrainian troops in Mariupol are dug into positions at the Azovstal Iron and Steel Works factory, where they have held out despite being largely surrounded and cut off from Ukrainian supply lines.

In a video address late Sunday, President Zelensky criticized Western countries for delaying weapon deliveries and called on them to do more to help the Ukrainian army. “We are doing everything to ensure defense,” Mr. Zelensky said. “But those who have the weapons and ammunition we need and delay their provision must know that the fate of this battle also depends on them. The fate of people who can be saved.”

The Azov Battalion, which has been holed up in the Azovstal steel plant, near the city’s coast, said it was continuing to fight on, pinning down Russian soldiers.

“Despite the overwhelming enemy forces, the Azov Regiment fighters are launching a counterattack,” the group said in a statement on Telegram.

Mariupol has sustained some of the heaviest damage of any Ukrainian city since Russia invaded.

Photo: ALEXANDER ERMOCHENKO/REUTERS

Shattered glass littered the ground at a damaged bus stop in Mariupol.

Photo: ALEXANDER ERMOCHENKO/REUTERS

Mr. Zelensky said Russian troops are preparing for an offensive operation in eastern Ukraine. Russia has deployed more military forces and equipment in and around eastern Ukraine in recent days, setting the stage for a new phase of Moscow’s offensive after Ukraine managed to thwart a Russian push toward the capital Kyiv and in other parts of the country.

“It will begin in the near future. They want to literally finish off and destroy Donbas,” Mr. Zelensky said. “Just as the Russian troops are destroying Mariupol, they want to wipe out other cities and communities.”

A child held a toy rifle next to destroyed Russian military vehicles near Chernihiv, in northern Ukraine.

Photo: Evgeniy Maloletka/Associated Press

The last Ukrainian troops in Mariupol are dug into positions at the Azovstal Iron and Steel Works factory.

Photo: ALEXANDER ERMOCHENKO/REUTERS

Russian officials Monday reported the death of Capt. Aleksandr Chirva, commander of the Ropucha-class landing ship Cesar Kunikov.

Two Ropucha-class ships were damaged when a Ukrainian missile hit the Russian-occupied port of Berdyansk in March, sinking a larger landing ship, Saratov.

Kremlin spokesman Dmitry Peskov said that negotiations with Ukraine are continuing but that progress was slow. Last week, Russian President Vladimir Putin said peace talks with Kyiv had reached a dead end.

“Contacts continue at the expert level within the framework of the negotiation process,” Mr. Peskov told reporters Monday. “The dynamics of the negotiation process leave much to be desired.”

Mr. Putin said Monday that sanctions imposed on Moscow over the Ukraine invasion have failed to undermine the country’s economy, saying that retail demand had normalized and unemployment had remained low.

Still, he acknowledged that consumer prices have risen significantly, with annual inflation hitting 17.5% as of April 8.

“These are very high values,” Mr. Putin said at a meeting with government ministers. “People feel this on their family budget, they feel how prices have risen, and we need to support our citizens, help them cope with the inflationary wave.”

Ukraine’s SBU security agency released a video of Viktor Medvedchuk, a Ukrainian ally of Mr. Putin captured in the Kyiv region last week, in which he appealed to Mr. Putin to exchange him for Ukrainian forces and residents in Mariupol. Mr. Medvedchuk headed a pro-Russian political party in Ukraine that authorities shut down after Russia invaded Ukraine. He had been on the run after having escaped house arrest on treason charges.

Messrs. Medvedchuk and Putin have long had a close relationship and Mr. Putin is the godfather to one of Mr. Medvedchuk’s children. On Monday, Mr. Peskov declined to comment on a separate appeal by Mr. Medvedchuk’s wife for a possible swap.

—Yaroslav Trofimov contributed to this article.

Write to Georgi Kantchev at georgi.kantchev@wsj.com, Thomas Grove at thomas.grove@wsj.com and Isabel Coles at isabel.coles@wsj.com