Ukrainian officials say their military’s southern offensive is going slowly. They also say that is precisely the plan.

The announcement Monday of a thrust in the south raised hopes that Ukraine could reclaim territory Russia seized early in the war, including the regional capital of Kherson.

But success could take many shapes, say officials and Western analysts. Even without quickly regaining much ground, Kyiv can achieve progress by forcing Russia to expose its troop locations and supply bases, take a defensive posture and thereby appear weak or pull troops from other parts of the country. Ukraine can also gain intelligence about Russian formations, vulnerabilities and will to fight.

Ukrainian officials say they have neither the armor nor the manpower to make a quick advance. Instead, the military aims to weaken front-line Russian forces while also using long-range artillery and rockets, such as Himars provided by the U.S., to hit critical installations behind Russian lines such as command posts and ammunition depots.

Kherson sits on the west bank of the Dnipro River, which Russian troops must cross to enter, resupply or leave the city. Ukraine’s military says its strikes on bridges across the Dnipro and the smaller Inhulets River to the city’s northeast have largely cut supply lines to Russian forces in the city.

Ukraine’s southern push could draw Russian resources away from other areas targeted in the invasion, such as the heavily shelled northeastern city of Kharkiv.

Photo: Anastasia Taylor-Lind for The Wall Street Journal

Russia has roughly 20,000 troops in and around Kherson, Western officials estimate, cautioning the figure isn’t precise. Trapping them could potentially force a surrender, allow Ukraine to decimate them or force them to flee. Whatever happens, Ukraine hopes to retake Kherson without having to engage in bloody street fighting.

Oleksiy Arestovych, a Ukrainian presidential adviser, called the strategy “the systemic grinding of Putin’s army.” He said Kyiv’s forces are working “to uncover their operational logistical supply system and destroy it with artillery and Himars,” a process that can take time.

“There’s no rush,” he said.

While Ukraine ultimately wants to evict Russian forces from Kherson—the city’s occupation is one of Moscow’s most significant gains since invading on Feb. 24—Kyiv could still boast of success if it retakes towns outside the city, captures or kills a large number of Russian troops or compels some to retreat.

The Kherson offensive also represents an element of Ukraine’s broader strategy to strain Russia’s entire invasion force, from around Kharkiv in the northeast to Crimea on the Black Sea.

By attacking in so many places, “you keep the Russians wondering where the Ukrainians are going to strike next,” said retired U.S. Army Lt. Gen. Stephen Twitty. “You want an unpredictable fight to keep the Russians on their heels.”

Gen. Twitty, who participated in Operation Desert Storm, said not to expect a massed attack.

Bridges across the Dnipro River have become key targets in Ukraine’s effort to cut supply lines to Russian forces in Kherson.

Photo: ALEXANDER ERMOCHENKO/REUTERS

“We’re going to see multiple locations of small units, which is going to wreak havoc on the Russians and is a great way to fight,” he said. But he cautioned: “In this type of fighting, you have to take a long-term perspective.”

Ukraine’s fighters may advance and pause to prepare for a subsequent attack, said Billy Fabian, a former U.S. Defense Department analyst. “You’re always thinking about the next operation.”

Ukrainian forces will move slowly because they are attempting an operation that military planners consider exceedingly difficult: dislodging an entrenched defender without overwhelming force or air superiority. Kyiv has a limited number of skilled or veteran troops and must deploy them across a vast front line. Ukrainian commanders want to put at risk the smallest number of troops possible.

Attempting “a deliberate storming of Kherson city would likely be a mistake,” said Jack Watling, a senior research fellow at the Royal United Services Institute, a British think tank, in an analysis posted Friday.

Instead, Ukraine is capitalizing on the region’s geography, aiming to push Russian troops against riverbanks. Ukrainian forces appear to be advancing on land from the north and west while increasing the tempo of strikes on bridges and supply facilities. Their goal is to starve Russian forces of supplies while closing in on them.

Long-range weapons such as the U.S.-supplied Himars have allowed Ukraine to reach behind Russian lines.

Photo: VIA PAVLO NAROZHNYY via REUTERS

“We need the enemy to be unable and unwilling to resist effectively,” said Mr. Arestovych, the Ukrainian presidential adviser.

Russian attempts to retreat across the rivers would make rich targets for Ukrainian drones, rockets and artillery.

Ukrainian forces appear already to have retaken some small towns outside Kherson, according to open-source intelligence reports. Gen. Twitty said the incremental gains count as a tactical success because “these little towns mean a lot” to Ukrainians, who see compatriots liberated, and to Kyiv’s Western backers, who want to see progress against Russia.

Ukraine’s larger strategic objective of regaining its land and repelling Russian forces is vital because the war is likely to end in some form of negotiation, Gen. Twitty said.

“The long-term perspective is, the more gains Ukraine can make, the better off they will be at the negotiating table,” he said.

—Stephen Fidler contributed to this article.

Write to Daniel Michaels at daniel.michaels@wsj.com and James Marson at james.marson@wsj.com