Efforts were underway to evacuate all remaining troops from their last stronghold in the ruined city of Mariupol as fighters that have held out for 82 days began to surrender, Ukraine's military said Tuesday, ceding control of the city to Russia after months of bombardment.

The evacuation of hundreds of fighters, many wounded, to Russian-held towns, likely marked the end of the longest and bloodiest battle of the Ukraine war and a significant defeat for Ukraine. Mariupol is now in ruins after a Russian siege that Ukraine says killed tens of thousands of people in the city.

Video released by the Russian ministry of defense showed fighters leaving the plant, some being carried on stretchers, others with their hands up to be searched by Russian troops.

Russia said 256 Ukrainian fighters had "laid down their arms and surrendered," including 51 severely wounded.

"The 'Mariupol' garrison has fulfilled its combat mission," the General Staff of Ukraine's Armed Forces said in a statement.

"The supreme military command ordered the commanders of the units stationed at Azovstal to save the lives of the personnel ... Defenders of Mariupol are the heroes of our time," it added.

The Ukrainian military avoided using the term "surrender" to describe the effort to pull out of the steel plant to save as many lives as possible. Officials planned to keep trying to save an unknown number of fighters who stayed behind. It was unclear if soldiers evacuated to Russian-controlled areas would be considered prisoners of war.

Ukraine said 264 soldiers, including 53 wounded, had left the metal plant. Ukrainian Deputy Defense Minister Anna Malyar said injured troops from the steelworks were taken to a hospital in the Russian-controlled town of Novoazovsk, some 32 kilometers (20 miles) to the east, while some of them were taken to the town of Olenivka, in an area controlled by Russian-backed separatists.

All of the evacuees will be subject to a potential prisoner exchange with Russia, she added.

About 600 troops were believed to have been inside the steel plant. Ukraine's military said efforts were underway to evacuate those still inside.

"We hope that we will be able to save the lives of our guys," Ukrainian President Volodymyr Zelenskyy said in an early morning address. "There are severely wounded ones among them. They're receiving care. Ukraine needs Ukrainian heroes alive."

Reuters saw five buses carrying troops from Azovstal arrive in Novoazovsk late on Monday. In one, marked with "Z" like many Russian military vehicles in Ukraine, men were stacked on stretchers on three levels. One man was wheeled out, his head tightly wrapped in thick bandages.

Heavy shelling reported

Ukraine made a symbolic gain when its forces reportedly pushed Russian troops back to the Russian border in the Kharkiv region. The video showed Ukrainian soldiers carrying a post that resembled a Ukrainian blue-and-yellow-striped border marker and then posing next to it. But fierce fighting and shelling continued across a broad area of the country's east.

Zelenskyy's office said on Tuesday the entire front line around Donetsk is under constant massive shelling, while in the northern region of Chernihiv, a missile strike on the village of Desna killed and wounded an unspecified number of people.

Ukraine's general staff said Russian forces were reinforcing and preparing to renew their offensive near Slovyansk and Drobysheve, southeast of the strategic town of Izyum, having suffered losses elsewhere.

Areas around Kyiv and the western city of Lviv, near the Polish border, have continued to come under Russian attack. A series of explosions struck Lviv early on Tuesday, a Reuters witness said. One missile hit a military facility but there were no casualties, according to Zelenskyy's office.

A village in Russia's western province of Kursk bordering Ukraine came under Ukrainian fire on Tuesday, regional Governor Roman Starovoit said. Three houses and a school were hit but there were no injuries, he said.

Russian border guards returned fire to quell the shooting from large-caliber weapons on the border village of Alekseyevka, Starovoit wrote on messaging app Telegram.

Moscow calls its nearly three-month-old invasion a "special military operation" to rid Ukraine of fascists, an assertion Kyiv and its Western allies say is a baseless pretext for an unprovoked war.

Putin climbdown over NATO

Zelenskyy planned to speak to German Chancellor Olaf Scholz and French President Emmanuel Macron on Tuesday, his office said.

Russia has faced massive sanctions for its actions in Ukraine, but EU foreign ministers failed on Monday to pressure Hungary to lift its veto of a proposed oil embargo.

German Finance Minister Christian Lindner said he is open to the idea of seizing Russian state assets to finance Ukraine's reconstruction.

McDonald's Corp. became one of the biggest global brands to exit Russia, laying out plans to sell all its restaurants after operating in the country for more than 30 years.

Russian President Vladimir Putin appeared on Monday to climb down from threats to retaliate against Sweden and Finland for announcing plans to join the U.S.-led NATO military alliance.

"As far as expansion goes, including new members Finland and Sweden, Russia has no problems with these states – none. And so in this sense, there is no immediate threat to Russia from an expansion to include these countries," Putin said.

The comments appeared to mark a major shift in rhetoric, after years of casting NATO enlargement as a direct threat to Russia's security, including citing it as a justification for the invasion of Ukraine itself.

Putin said NATO enlargement was being used by the United States in an "aggressive" way to aggravate an already difficult global security situation and that Russia would respond if the alliance moved weapons or troops forward.

Finland and Sweden, both nonaligned throughout the Cold War, say they now want the protection offered by NATO's treaty, under which an attack on any member is an attack on all.

Finland and Sweden's plans, however, hit a snag when NATO member Turkey's President Recep Tayyip Erdoğan said he would not approve either bid.