Ukraine rejected Russian demands to relinquish Mariupol's port city on Monday. Their people are surrounded by a humanitarian catastrophe that is growing pressure on European leaders to toughen sanctions against Moscow.

Ukraine's leadership stubbornly rejected Russian demands that Ukrainian forces in Mariupol lay down their arms in exchange for safe passage out of the city and the opening of humanitarian corridors on Monday at 1000 Moscow time.

"There can be no question of any surrender, laying down of arms," Ukraine's Deputy Prime Minister Iryna Vereshchuk said by the Ukrainska Pravda news outlet.

"We have already informed the Russian side about this."

Mariupol has been subjected to some of the most barrages since Russia invaded Ukraine on February 24. Many of the city's 400,000 citizens remain stranded as street rioting rages around them.

According to Vereshchuk, more than 7,000 people were evacuated from Ukrainian cities on Sunday via humanitarian corridors, with more than half coming from Mariupol. She indicated that the administration intended to send roughly 50 buses there on Monday to facilitate additional evacuations.

Russia and Ukraine have agreed on humanitarian corridors to evacuate civilians throughout the war but have frequently accused one another of violating them.

Mariupol and other damaged Ukrainian cities are set to dominate conversations this week between European Union leaders as they explore toughening penalties against Russia, including an oil embargo.

Russian soldiers pushing from the northeast towards Ukraine's capital Kyiv have paused, British intelligence warned on Monday.

Russian shells struck homes and a business sector in Kyiv's Podil district late Sunday, local police reported, following a relative calm in combat.

EU foreign ministers will resume discussions on Monday, ahead of US Vice President Joe Biden's arrival in Brussels on Thursday for summits with NATO's 30 allies, the EU, and in a Group of Seven (G7) format that includes Japan.

According to diplomats, the Baltic states, notably Lithuania, are pressing for an embargo as the next natural step, while Germany cautions against moving prematurely given Europe's already high energy prices.