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."

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

Ukrainian President Volodymyr Zelenskyy said Tuesday that a child has died from dehydration in the besieged port city of Mariupol.

"Russia is for sure to blame for the deaths of people from airstrikes and in the blocked cities," Zelenskyy said in a televised address. "But the responsibility is also on those who during these 13 days can't make a decision in their offices in the West, an obviously necessary decision. Those who don't secure Ukrainian sky from Russian murderers, who didn't save our cities from airstrikes, these bombs and missiles, although they can."

"We have been hearing promises about support for 13 days that the jets are about to arrive," he added. "We have heard promises about securing humanitarian corridors. They didn't work. We don't have time to wait. People in Mariupol don't have time to wait."

Zelenskyy said trucks carrying humanitarian aid have been sent to Mariupol. He accused the International Committee of the Red Cross of "forbidding the use of its emblem on our cars," but did not give further details. Videos posted to social media on Tuesday purportedly show vehicles heading to Mariupol from other Ukrainian cities bearing signs with a red cross, but it's not clear who pasted them there.

"The drivers are heroes who understand they can be killed by Russian troops," Zelenskyy said. "If you kill those people, the whole world will be the witness."

-ABC News' Julia Drozd