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

The Russian Ministry of Defense claimed Tuesday that Ukrainian authorities are "categorically against" evacuating residents of Kyiv, Chernihiv, Sumy, Kharkiv and Mariupol to Russia.

"The authorities in Kyiv are continuing to categorically reject all main routes of evacuation from Kyiv, Chernihiv, Sumy, Kharkiv, and Mariupol to the territory of the Russian Federation," Mikhail Mizintsev, head of the Russian National Defense Control Center, said at a press briefing.

The Russian defense ministry alleged that the Ukrainians only confirmed one of the 10 evacuation routes Russia proposed. The confirmed route is from the city of Sumy, through Poltava and to the border with Poland, Mizintsev said.

The Russian defense ministry also claimed that more than 2.5 million Ukrainians have asked to be evacuated to Russia.

"Following the past day, 2,541,367 appeals from individual Ukrainian citizens, as well as foreigners made via various communication channels requesting to save and evacuate them from 1,917 settlements in Ukraine have already been processed in our database," Mizintsev said.

The Russian defense ministry further alleged that checkpoints in Poland, Slovakia, Hungary, Moldova and Romania "were virtually ill prepared" to receive Ukrainian refugees.

"People are forced to leave their cars and walk on foot carrying their heavy bags. Lines are up to 40 kilometers long, and the crossing time is over two days," Mizintsev said.

Vatican secretary of state, Cardinal Pietro Parolin, spoke on the phone with the Russian foreign minister to convey Pope Francis' "deep concern about the ongoing war in Ukraine."

Parolin reiterated the pope's "call for an end to armed attacks, for the securing of humanitarian corridors for civilians and rescuers, and for the replacement of gun violence with negotiation."

The pope announced Sunday that he has dispatched two cardinals to Poland and Hungry. Cardinal Konrad Krajewski traveled to the Polish-Ukraine border to visit refugees and volunteers in shelters and homes, while Cardinal Michael Czerny will arrive in Hungry on Tuesday to visit reception centers for migrants arriving from Ukraine.

-ABC News' Phoebe Natanson

While the United States welcomes Russia's declaration of a temporary cease-fire in several besieged areas of Ukraine, Pentagon Press Secretary John Kirby said Tuesday it remains unclear exactly how long Russian forces will hold fire.

"We think this is obviously a welcome step that the cease-fire seems to be being observed by the Russians. They don't exactly have a good track record in that regard. So it's welcome to see people are able to get out," Kirby told ABC News' George Stephanopoulos in an interview on "Good Morning America."

"But," Kirby added, "that cease-fire's going to expire in a number of hours and so it's yet to be seen how much more violent the shelling and the bombardments are going to get."

While Ukraine has continued to call on NATO to establish a no-fly zone over the country -- something Washington has already ruled out -- along with more help from the U.S., Kirby said there are other steps being taken.

"We are accelerating and expediting the shipment of arms and materiel to Ukraine. In fact, another shipments arrived in eastern Europe just overnight and they will be sent in to Ukraine in the coming hours and days, and there's more coming," Kirby said. "And it's not just the United States. Fourteen other nations are also providing security assistance to Ukraine to help them fight."

But on the potential of the U.S. replacing Polish fighter jets, should Poland send theirs to Ukraine, Kirby said it was a "possibility" but was non-committal.

"We're not going to stand in the way of another sovereign nation if they want to provide aircraft to the Ukrainian Air Force. Now that's certainly their decision and we respect that," he said. "This issue of whether we backfill it with American jets -- we're looking at that as a possibility here, but there's an awful lot of logistical and financial issues that have to be dealt with on how that would happen. No decision has been made yet."

When asked about the risk of a wider war if that happens, Kirby said: "That's a possibility that we're always looking at."

"That's certainly in the back of everybody's mind, not just the United States but in NATO nations as well. You don't want to escalate this conflict any bigger and any worse than it already is. You're talking about Russia, a nuclear armed power. The consequences for escalating this conflict could be devastating, not just for the people of Ukraine but for the European continent."

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Pentagon press secretary talks US plan to help Ukraine amid Russian attacks

John Kirby answers questions about the intensifying attacks from Russian forces and the administration’s latest efforts to help Ukraine.

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The White House is expected to announce a ban on U.S. imports of Russian oil as soon as Tuesday, a source familiar with the matter told ABC News.

-ABC News' Cecilia Vega