Russia-Ukraine updates: Putin says 'certain positive movements' in negotiations

Ukrainian President Volodymr Zelenskyy on Saturday claimed that more than 10,000 Russian army troops have been killed in the war.

"It's young men, 18 to 20-year-old boys, who lost their lives having no idea why their country sent them to war," Zelenskyy said during a speech.

"We're inflicting such heavy losses on the enemy that they couldn't have imagined in their worst nightmares," Zelenskyy said.

He said Ukraine is managing to hold the line on all key fronts and directions and that the Ukrainian army has gone on counterattack in Kharkiv.

Zelenskyy also thanked Polish President Andrzej Duda for the country's support which helped prevent a humanitarian crisis at the border.

"There's practically no border between Ukraine and Poland any more," Zelenskyy said.

The Ukrainian president said he has already begun discussions on post-war reconstruction efforts.

"I spoke to World Bank President and IMF managing director, and we have an agreement on measures to support Ukraine. Tens of billions of dollars will be provided for renovation after the war, and that's just the beginning," Zelenskyy said.

"I'm grateful to Americans, to bipartisan support in the U.S. Congress, but also to millions of ordinary people who call for tougher sanctions against the aggressor and better protection of Ukraine," Zelenskyy said.

-ABC News' Fidel Pavlenko

Russian President Vladimir Putin on Saturday dismissed the idea of imposing a "no-fly" zone over Ukraine, which Ukrainian President Volodymr Zelenskyy has been calling for.

"It's impossible to do it, any attempts by other countries to do it will be regarded as their participation in military conflict," Putin said Saturday while speaking to female pilots and stewardesses from Russia’s national airline Aeroflot.

Putin claimed that Ukrainian “neo-Nazis” were not allowing people to leave Ukrainian cities in order to use them as human shields. The Red Cross on Saturday confirmed that the evacuations were stopped because of Russian shelling.

Putin also commented on the sanctions the West imposed on Russia, calling them "akin to a declaration of war," but insisted that Russia could adapt and suggested the countries imposing them would reverse because it also hurt their interests.

On the invasion of Ukraine, Putin claimed again that it was going "according to plan, to schedule." He also claimed that Russia was only using professional soldiers, not conscripts in Ukraine and would continue to do so.

Talks with Ukraine are continuing, according to Putin, with Russia's key demand being the "de-militarization" of Ukraine.

Putin also made threatening comments about Ukraine's statehood.

"Especially those from today's leadership, should understand that if they continue doing what they are doing, they call into question the future of Ukrainian statehood. And if it happens it will be wholly and fully on their conscience," Putin said.

Putin said there is no current plan to implement martial law in Russia and would only do so in the case of “outside aggression” against specific regions of Russia.

Putin also suggested that Russia might try to block international airlines from flying over Siberia, which would disrupt international airlines trying to fly from Europe to Asia.

-ABC News' Patrick Reevell and Somayeh Malekiah

U.S. Secretary of State Antony Blinken said Saturday his visit to Poland comes at "one of the most urgent moments in the long history of friendship between our two countries."

Speaking at a joint press conference with Polish Foreign Minister Zbigniew Rau in the southeastern city of Rzeszow, Blinken said the ideals that bind Poland and the United States are "under threat in this region like never before."

"We will stand together, as we've been standing together, in support of Ukraine and against Russia's unprovoked unwarranted premeditated invasion," Blinken told reporters.

Out of the more than 1.36 million people who have been forced to flee Ukraine since Russian forces invaded on Feb. 24, over 756,000 have crossed into neighboring Poland, according to the latest figures from the United Nations High Commissioner for Refugees (UNHCR).

Blinken noted that "at this moment of crisis for millions of Ukrainians and as the security of Europe hangs in the balance," it's an "incredibly powerful reflection of Poland's values that those fleeing the war will find refuge in Poland."

He outlined U.S. funding to support the needs of Ukrainian refugees in Poland and other countries, including a $2.75 billion requested aid package and the $54 million in humanitarian assistance announced last week.

Meanwhile, Rau warned Russia that Poland would not recognize any territorial transfers taken by force. He told reporters that Russian shelling of residential areas and a nuclear power plant in Ukraine "are war crimes under international law" and should "be prosecuted with utmost determination."

The U.S. has yet to say whether Russia has engaged in war crimes in Ukraine.

-ABC News' Justin Gomez

A senior U.S. official told ABC News on Saturday that they have no doubt Russia's indiscriminate bombing of Ukraine will increase in the coming days.

When asked how long they think Ukraine can hold out, the official said Ukrainian forces as a "whole" are degrading but are strong and growing as individuals or "partisans." At least 500 "fighters" from elsewhere crossed into Ukraine on Friday to join the fight against Russia, according to the official.

-ABC News' Martha Raddatz