Firefighters extinguish a fire in an oil depot caused by Russian strikes in Zhytomyr, Ukraine. Reuters

Russian aircraft bombed cities in eastern and central Ukraine overnight, Ukrainian officials said. Shelling pounded suburbs of the capital, Kyiv.

Meanwhile, Russian officials said they planned to carry out a limited cease-fire on Tuesday to allow civilians to safely flee besieged Ukrainian cities - something Ukrainian officials said they would believe only after safe evacuations begin, after two earlier attempts at cease-fires failed.

In Sumy and Okhtyrka, to the east of Kyiv near the Russian border, bombs fell on residential buildings and destroyed a power plant, regional leader Dmytro Zhivitsky said. He said there were dead and wounded but gave no figures.

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Bombs also hit oil depots in Zhytomyr and the neighboring town of Cherniakhiv, located west of Kyiv.

The humanitarian crisis in Ukraine grew Monday amid intensified shelling by Russian forces. Food, water, heat and medicine grew increasingly scarce in some areas, including the port city of Mariupol. Russian and Ukrainian delegations held a third round of talks, and a top Ukrainian official said minor, unspecified progress was made toward establishing safe corridors for civilians to escape.

Bombs also hit oil depots in Zhytomyr and the neighboring town of Cherniakhiv, located west of Kyiv. Reuters

In Bucha, a Kyiv suburb, the mayor reported heavy artillery fire.

"We can’t even gather up the bodies because the shelling from heavy weapons doesn’t stop day or night,” Mayor Anatol Fedoruk said. "Dogs are pulling apart the bodies on the city streets. It’s a nightmare.”

The Ukrainian government is demanding the opening of humanitarian corridors to allow people to safely leave Sumy, Zhytomyr, Kharkiv, Mariupol and suburbs of Kyiv, including Bucha.

Ukraine President Volodymyr Zelenskyy speaks in Kyiv, Ukraine, on Sunday. AP

Ukrainian President Volodymyr Zelenskyy urged his people to keep resisting the assault, which U.N. officials say has forced more than 1.7 million people from Ukraine. Zelenskyy also called for a global boycott of all Russian products, including oil.

The mayor of Lviv said the city in far western Ukraine is struggling to feed and house the tens of thousands of people who have fled here from war-torn regions of the country.

"We really need support,” Mayor Andriy Sadovyi said.

More than 200,000 Ukrainians displaced from their homes are now in Lviv, filling up sport halls, schools, hospitals and church buildings. The historical city once popular with tourists had a population of 700,000 before the war.

A woman carrying her baby crosses a destroyed bridge as they flee the city of Irpin on Monday. AFP

The mayor said the city needs big tents equipped with kitchens so food can be prepared.

Hundreds of thousands more people could arrive if humanitarian corridors are opened up from cities now under siege from Russian troops.

The embassies of the U.S. and EU countries also moved to Lviv from Kyiv before the invasion.

Lviv is the main transit point for those fleeing just across the border to Poland. Many of the 1.7 million Ukrainians now abroad passed through the city. The United Nations has called the situation the fastest growing refugee crisis in Europe since World War II.