BERLIN >> President Vladimir Putin of Russia on Friday insisted that Ukraine order some of its forces to surrender to Russia, a striking demand made hours after President Donald Trump said the United States had “very good and productive” discussions with Putin about a potential ceasefire in Ukraine.

Putin’s televised comments came shortly after Trump, on social media, said he had urged the Russian leader to spare the lives of Ukrainian soldiers struggling to hold on to a patch of land in the Kursk region of Russia.

“I have strongly requested to President Putin that their lives be spared,” Trump wrote.

Both presidents claimed Friday that Ukrainian forces were surrounded in Kursk, the area where Kyiv’s troops stunned Russia with a cross-border incursion over the summer. Independent analysts have challenged those claims, and Ukraine’s military Friday again rejected them.

Still, Russian forces have of late had the upper hand in the fighting in Kursk. And Putin said that for Trump’s call “to be effectively implemented,” the leaders of Ukraine needed to order “its military units to lay down their arms and surrender.” Neither man has raised the idea of Russian troops on Ukrainian land surrendering.

President Volodymyr Zelenskyy of Ukraine gave no indication Friday that his country’s soldiers would withdraw from Kursk, let alone surrender, but acknowledged that the situation in the region was “very difficult.”

He also questioned whether Russia was acting in good faith, accusing Putin of “doing everything possible to ensure that diplomacy fails.” Ukraine, Zelenskyy reiterated, has already agreed to a 30-day, unconditional ceasefire to stop the war that Russia’s leader began by ordering the full-scale invasion three years ago.

“Putin cannot get out of this war, because then he will be left with nothing,” Zelenskyy wrote on social media. “That is why he is now doing everything possible to sabotage diplomacy, setting extremely difficult and unacceptable conditions from the very beginning, even before the ceasefire.”

Battles have been raging in Kursk as Moscow’s forces push to drive Ukrainian troops from the land they seized over the summer. Russian troops have advanced in recent days, with Putin urging them to finish the job “in the shortest possible time.”

What happens next in Kursk has become a key point of contention before a potential ceasefire. Putin had on Thursday suggested less explicitly that he wanted Ukraine to order its soldiers there to surrender as part of any deal to end the war, which has killed and wounded more than 1 million soldiers and countless civilians over three years of grinding fighting.

But his comments Friday were far more direct, and came as both the Kremlin and White House signaled negotiations were moving forward despite the raft of concessions Moscow appears to be seeking.

After the Russian leader met with Steve Witkoff, the U.S. special envoy, in Moscow, late Thursday, top officials at both the White House and the Kremlin expressed “cautious optimism.”

“We had very good and productive discussions with President Vladimir Putin of Russia yesterday,” Trump wrote Friday morning on his Truth Social platform, in an apparent reference to the meeting with Witkoff. “There is a very good chance that this horrible, bloody war can finally come to an end.”

It wasn’t immediately clear whether Putin and Trump had spoken directly. The Kremlin had said that Putin, in his meeting with Witkoff, “passed along information and additional signals for President Trump.” It also said that Putin expected to talk to Trump but that the call had yet to be scheduled.

In that Truth Social post, Trump also said thousands of Ukrainian troops were “completely surrounded by the Russian military” — an apparent reference to Russian claims that Ukrainian soldiers were surrounded in Kursk.

“There is no threat of encirclement of our units,” the Ukrainian military’s general staff said in a statement soon after, calling such reports “false and fabricated by the Russians.”

A Ukrainian soldier fighting in Kursk who was reached by phone Friday, speaking on condition of anonymity to discuss the current situation on the battlefield, said “the situation is bad, almost critical.” But it was not as bad as Trump described in his post, the soldier added.

Ukrainian authorities Friday ordered several villages in the Sumy region, across the border from Kursk, to evacuate amid fears that the fighting could spill over.

“Aerial attacks — such as glide bombs and drones — have intensified in the border areas,” Volodymyr Artiukhin, the Ukrainian head of the Sumy Regional Military Administration, said on Facebook, announcing the mandatory evacuation of eight villages.

If Russian forces drive Ukrainian troops out of Kursk would deny Zelenskyy a significant bargaining chip in any negotiations.

And Putin showed Thursday that he was in no hurry to accept the offer of a 30-day truce made by Ukraine and the United States this week — telling a news conference that he was open to the proposal, but adding that he would seek to negotiate over a slew of issues, such as Western weapons deliveries to Ukraine, that could delay or derail any deal.

Dmitry Peskov, Putin’s spokesperson, suggested Friday that the outcome of the diplomatic back-and-forth would only become clear after Witkoff had briefed Trump and after the Russian and American leaders had spoken by phone. The two leaders are last known to have spoken Feb. 12.