KHARKIV, Ukraine — Ukrainian troops piled pressure on retreating Russian soldiers Tuesday, pressing deeper into occupied territory and sending more Kremlin forces fleeing ahead of the counteroffensive that has inflicted a stunning blow to Moscow’s military prestige.

As the advance continued, Ukraine’s border guard services said the army took control of Vovchansk — a town only two miles from Russia that was seized on the war’s first day. Russia acknowledged that it has withdrawn troops from areas in northeastern Ukraine’s Kharkiv region in recent days.

Russian troops were also pulling out from Melitopol, the second-largest city in southern Ukraine’s Zaporizhzhia region, the city’s pre-occupation mayor said. His claim could not immediately be verified.

Melitopol has been occupied since early March. Capturing it would give Kyiv an opportunity to disrupt Russian supply lines between the south and the Donbas region in the east, the two major areas where Moscow-backed forces hold territory.

Melitopol Mayor Ivan Fedorov wrote on the messaging app Telegram that the Russian troops were heading toward Crimea, which Moscow annexed illegally in 2014. He said columns of military equipment were reported at a checkpoint in Chonhar, a village marking the boundary between the Crimean peninsula and the Ukrainian mainland.

In the newly freed village of Chkalovske in the Kharkiv region, Svitlana Honchar said the Russians’ departure was sudden and swift.

“They left like the wind,” Honchar said Tuesday after loading cans of food aid into her car. “They were fleeing by any means they could.”

Some Russians appeared to have been left behind in the hasty retreat. “They were trying to catch up,” she said.

It was unclear yet whether the blitz by Ukraine, which unfolded after months of little discernible movement, could signal a turning point in the nearly seven-month war. But the country’s officials were buoyant, releasing footage showing their forces burning Russian flags and inspecting abandoned charred tanks. In one video, border guards tore down a poster that read, “We are one people with Russia.”

Momentum has switched back and forth before, and the U.S. warned against declaring a premature victory since Russian President Vladimir Putin still has troops and resources to tap. In the face of Russia’s largest defeat since its botched attempt to capture Kyiv early in the war, Russian Defense Ministry spokesman Igor Konashenkov said troops were hitting back with “massive strikes” in all sectors. But there were no immediate reports of a sudden uptick in Russian attacks.

Ukrainian President Volodymyr Zelensky said that his forces were carrying out “stabilization measures” across recaptured territory in the south and east, and rounding up Russian troops, “saboteurs” and alleged collaborators.

In his nightly address, Zelensky also pledged to restore normality in the liberated areas.

“It is very important that together with our troops, with our flag, ordinary, normal life enters the de-occupied territory,” he said, citing an example of how people in one village had already begun receiving pension payments after months of occupation.

As Russian troops pulled out, reports of chaos abounded — as well as claims that they were surrendering en masse. The claims could not be immediately verified.

Ukrainian Deputy Minister of Defense Hanna Maliar said Kyiv was trying to persuade even more Russian soldiers to give up, launching shells filled with fliers.

Russia uses “you as cannon fodder.... You don’t need this war. Surrender to Armed Forces of Ukraine,” the fliers read.

In the wake of the re- treat, Ukrainian authorities moved into several areas to investigate allegations of atrocities committed by Russian troops against civilians.

Since Saturday, the Kharkiv regional police have reported that local officers have found civilian bodies bearing signs of torture. It was not possible to verify their statements.