Russian President Vladimir Putin spoke with European Council President Charles Michel on Monday and according to a Kremlin readout of the conversation, falsely claimed Russian forces are “taking all possible measures to save the lives of civilians" in Ukraine.

Putin also repeated the Russian military’s claim that Ukrainian "nationalists" are preventing humanitarian corridors from being opened to allow the evacuation of civilians. But Ukrainian authorities have claimed efforts to evacuate its citizens out of the country have been disrupted by Russian forces shelling the humanitarian corridors Moscow agreed to in a cease-fire.

"The main threat comes from nationalist formations, which essentially use the tactics of terrorists, hiding behind the civilian population," Putin told Michel, according to the report.

The Russian president "called on the European Union to make a real contribution to saving people's lives, to put pressure on the Kyiv authorities and force them to respect humanitarian law," the Kremlin said in a statement.

-ABC News' Patrick Reevell

Ukrainian Minister of Foreign Affairs Dmytro Kuleba on Monday called for NATO to enforce a no-fly zone over Ukraine, saying Russian planes were targeting civilians.

"The Russian Air Force dominates in the skies and continues bombing our cities and killing many civilians," Kuleba told George Stephanopoulos on "Good Morning America."

U.S. and NATO officials have rejected calls from Ukrainian officials to impose a no-fly zone, saying doing so could provoke Russia, perhaps pulling other European countries and NATO members into the conflict. The U.S. and NATO have offered other military aid, including a possible deal to send aircraft to Ukraine.

"We believe that the rejection of the idea of the no-fly zone is based in the lack of confidence in the strength of NATO as an alliance," Kuleba said. "Because the military might of NATO is incomparably bigger compared to Russia. So why would Russia dare to shoot down a NATO plane, knowing it is doomed, eventually doomed, if a war with NATO begins."

Kuleba over the weekend had urged the international community to help in the struggle against “Russian barbarians.” He posted a photo on Twitter on Sunday of an unexploded bomb, which he said landed on a residential building in Chernihiv.

Ukrainian officials said Russia’s proposal on Monday to open "humanitarian corridors" for cities in Ukraine is not a genuine offer because it offers to evacuate civilians only to Belarus and Russia.

Iryna Vereshchuk, a Ukrainian vice prime minister, in a televised briefing called that "unacceptable" and said Ukraine had demanded instead that civilians be allowed to evacuate to other parts of Ukraine.

Russia’s Defense Ministry had said it would open a corridor from towns and villages north of Kyiv, where heavy fighting is taking place, but that would allow people to travel to the Belarusian city of Gomel and then be flown to Russia. Russia also offered corridors near the besieged northeastern and eastern cities of Kharkiv, Sumy and Mariupol, but that would also only allow people to leave over the border to Russia.

"This is an unacceptable option of humanitarian corridors. Our people from outskirts of Kyiv won’t go to Belarus and then to Russia," Vereshchuk said.

She said that Ukraine wants civilians north of Kyiv to be permitted to leave to the capital and for those from Kharkiv to be allowed to western cities by train, and from Mariupol north to the central city of Zaporizhzhia.

"We delivered our proposal on how the corridors should be organized," Vereshchuk said, later adding, "Humanitarian aid is prepared for a number of towns in the east and south. We ask Russia to confirm these corridors and provide ceasefire."

Russia has repeatedly violated its own ceasefire since offering humanitarian corridors for Mariupol and another eastern town Volnovakha, including shelling evacuation points in Mariupol according to officials there. The Red Cross, which is trying to organize the evacuations, has said the agreements currently are too vague and without clear understandings for routes out.

Russia said Monday's offer for the corridors was made following a lengthy phone conversation between French President Emmanuel Macron and Russian President Vladimir Putin on Sunday.

Vereshchuk said Russia was trying to exploit Macron’s name for a disingenuous offer of corridors.

"I hope president Macron understands that his name and good intentions are manipulated by Russia," she said.

-ABC News’ Patrick Reevell

More than 1 million people fleeing Ukraine have arrived in Poland since the Russian invasion began on Feb. 24, the Polish Border Guard said on Monday.

A record 142,000 people arrived on Sunday, the guard said on Twitter. On Monday, about 42,000 people had crossed the border before 7 a.m. local time.

As of Sunday, more than 1.5 million people had fled the war in Ukraine, marking the "fastest growing refugee crises in Europe since World War II," according to Filippo Grandi, the U.N. high commissioner for refugees.

The Russian forces charging toward Kyiv haven't made progress in the last day as they face Ukrainian resistance and low food and gas supply, a senior U.S. defense official told reporters Tuesday.

However, it could be a deliberate pause, the official said. "Part of the stall could be ... as a result of their own self-determined sort of pause in operations -- that they are possibly regrouping, rethinking, reevaluating," the official said.

The U.S. believes Russian forces "have committed now more than 80% of what was their pre-staged combat power," the official added.

The official said some Russian soldiers weren't told they were going into combat. The official said "not all of them were apparently fully trained and prepared."

The strong Ukrainian resistance has also hurt morale, according to the official.

Russia has now launched more than 400 missiles on Ukraine, the official said. The U.S. believes Russia has launchers that could be used for thermobaric weapons, but cannot confirm their use, the official said.

Russian forces are making the most progress in the south. Russians are attacking Kherson in south Ukraine, which "appears very much to be contested city at this point," the official said.

Russians are also approaching Mariupol in southeastern Ukraine, and while they haven't yet entered the city, "they are close enough now that they could attack Mariupol with long range fires," the official said.

Two towns on the path to Mariupol are believed to be occupied by the Russians, according to the official.

The U.S. believes the Russians hope to move north out of Mariupol up to the heavily-contested city of Kharkiv. The official said they believe Russian forces are trying to encircle Kharkiv.

The U.S. official noted that they've seen "certain risk-averse behavior by the Russian military" over the last week.

"Take the amphibious assault, for instance. They put those troops ashore a good 70 kilometers away from Mariupol because they knew Mariupol was going to be defended and they could put them ashore in an uncontested environment. And they still haven't reached Mariupol," the official said.

"They are not necessarily willing to take high risks with their own aircraft and their own pilots," the official said.

"And of course we're seeing that on the ground -- the fairly slow and steady progress that they have made, and you guys are seeing it for yourselves on the ground where ... units are surrendering, sometimes without a fight."

-ABC News' Matt Seyler