Russian shells hit houses and a shopping district in Kyiv's Podil district late on Sunday killing at least four people, city authorities said, following a relative lull in the fighting over the weekend.
"There can be no question of any surrender, laying down of arms," said Deputy Prime Minister Iryna Vereshchuk in response to Moscow's offer to let Mariupol residents leave the city if they surrender their weapons.
"We have already informed the Russian side about this," said Vereshchuk, according to the Ukrainska Pravda news portal.
Western countries say Russia's expectations of a swift victory and the removal of President Volodymyr Zelenskiy's government have been dashed and its invasion force has got bogged down.
Ukraine and its Western backers say Russian ground forces have made few advances in the past week, concentrating their efforts on artillery and missile strikes - often into urban centres.
The bulk of Russian forces remain more than 25km from the centre of the Kyiv, British military intelligence said.
"Heavy fighting continues north of Kyiv," the Ministry of Defence said. "Forces advancing from the direction of Hostomel to the northwest have been repulsed by fierce Ukrainian resistance."
Russian President Vladamir Putin says the biggest attack on a European state since World War II is "a special military operation" to stop the Ukrainian government from committing "genocide" - an accusation the West calls a baseless fabrication.
The humanitarian crisis in the port city of Mariupol, where residents are besieged with little food, water and power, is increasing pressure on European leaders to toughen sanctions on Moscow.
Russia offered to open humanitarian corridors from the city from 10am on Monday if residents lay down arms. Russia and Ukraine have made agreements throughout the war on exit corridors but accuse each other of violations.
Vereshchuk said more than 7000 people were evacuated from Ukrainian cities through humanitarian corridors on Sunday, more than half from Mariupol. She said the government planned to send nearly 50 buses there on Monday for more evacuations.
European Union leaders this week will meet to consider imposing tougher sanctions on Russia including an oil embargo.
EU ministers will take up the discussion on Monday before US President Joe Biden arrives in Brussels on Thursday for summits with NATO's 30 members, as well as the EU and in a Group of Seven (G7) format including Japan.
In his latest appeal for help from abroad, Ukrainian President Volodymyr Zelenskiy addressed the Israeli parliament by video link on Sunday and questioned Israel's reluctance to sell its Iron Dome missile defence system to Ukraine.
"Everybody knows that your missile defence systems are the best ... and that you can definitely help our people, save the lives of Ukrainians, of Ukrainian Jews," said Zelenskiy, who is of Jewish heritage.
Zelenskiy also welcomed the mediation efforts of Israeli Prime Minister Naftali Bennett, who has held numerous calls with him and Putin.
"Sooner or later we will begin to have talks with Russia, possibly in Jerusalem," he said in his daily video address to Ukrainians.
Negotiators reported some progress last week on a political formula that would guarantee Ukraine's security, while keeping it outside NATO - a key Russian demand - though each side accused the other of dragging things out.
Mariupol's council said on Telegram that several thousand residents had been "deported" to Russia over the past week. Russian news agencies said buses had carried hundreds of refugees from Mariupol to Russia in recent days.
US ambassador to the United Nations Linda Thomas-Greenfield told CNN the deportation accounts were "disturbing" and "unconscionable" if true.
The UN human rights office said at least 902 civilians had been killed as of Saturday, though the real toll was probably much higher.
About 10 million Ukrainians had been displaced, including some 3.4 million who have fled to neighbouring countries, the UN refugee agency said.
