At least 18 people have now been killed and more than 100 wounded after shelling in the centre of Kharkiv, according to Ukrainian President Volodymyr Zelenskyy, as the south-eastern port city of Mariupol looked on the brink of falling to Russia.
And the start of the new week saw multiple explosions hit the western city of Lviv, according to Mayor Andriy Sadovyi.
He said five missiles struck Lviv on Monday morning, with emergency services responding to the blasts.
The day earlier, regional authorities announced five people were killed and 20 were injured when a missile and artillery fire hit central Kharkiv and the Saltivka suburb, adding to earlier casualties over the previous three days.
Ukrainian Foreign Minister Dmytro Kuleba said there have not been any recent diplomatic communications with Russia at the foreign ministry level and that the "dire" situation in Mariupol may halt the path of negotiations.
Russia estimated 2,500 Ukrainian fighters were holding out at a steel plant in the last pocket of resistance in Mariupol, much of which has been reduced to a smoking ruin during a seven-week siege.
Moscow gave the city's defenders a surrender-or-die ultimatum with a Sunday, saying those who laid down their arms were "guaranteed to keep their lives".
But the fighters ignored the demand, just as they had rejected previous ultimatums.
The British government has said its support for Ukraine is "resolute" after the Kremlin imposed travel bans on Prime Minister Boris Johnson and other senior officials.
'Easter of war' as Russian strikes continue across Ukraine
Major population centres across Ukraine were struck by Russian assaults over the Easter weekend.
Regional governor Oleh Synehubov said that Kharkiv's city centre and the Saltivka suburb were hit by rocket launcher and artillery fire, causing casualties and destroying apartment blocks.
Mr Synehubov said Ukraine's armed forces had successfully engaged in counter-attacks in the Kharkiv region, recapturing two villages fully and another partially.
Kharkiv Mayor Igor Terekhov urged the city's residents to take shelter and leave if possible, as they were defending their "lives and honour fighting against the ruthless army of the aggressor".
"Today is a big Orthodox holiday, Palm Sunday … even days that are sacred to Christians are no reason for the enemy to lessen bombardments on Kharkiv," he said.
"We are moving people to places that are less dangerous because there are no longer any fully safe places in Kharkiv. There we provide a place to live, hot food, shower, medical help."
Local media reported an explosion in Kyiv, although deputy mayor Mykola Povoroznyk said air defence systems had thwarted Russian attacks.
The mayor of Brovary city, close to Kyiv, said a missile attack had damaged infrastructure.
Russia said it had destroyed an ammunition factory near the capital.
As clean-up operations continued in areas where the Russians have retreated, Ukraine's human rights ombudswoman said almost all high-rise buildings in the town of Okhtyrka were unfit for occupation.
Authorities said 41 bodies had been recovered in the town of Borodyanka.
Most Ukrainians celebrate Orthodox Easter next Sunday, but in Bucha — a town north of Kyiv where Ukraine accuses Russia of killing dozens of civilians — some 50 people attended a church service, carrying pussy willow and praying for the dead.
Russia denies targeting civilians and has called images from Bucha fake.
"I just prayed today to stop crying," said resident Evgeniya Lebedko after the service.
Meanwhile, during the papal address in St Peter's Square after Mass on Sunday, Pope Francis Implicitly criticised Russia, pleading for an end to the bloodshed and lamenting the "Easter of war".
"May there be peace for war-torn Ukraine, so sorely tried by the violence and destruction of the cruel and senseless war into which it was dragged," he said.
Mr Zelenskyy accused Russia on Saturday of "deliberately trying to destroy everyone" in Mariupol.
Despite the desperate situation in Mariupol, Ukraine said it was holding off Russian forces in other parts of the Donbas regions of Donetsk and Luhansk, which before the invasion were already partly controlled by Russian-backed separatists.
Police in the Donetsk region said that during the past 24 hours, Russian forces had opened fire from tanks, multiple rocket launchers and heavy artillery on 13 settlements under Ukrainian control, killing two civilians.
Luhansk governor Sehriy Gaidai said that, since the start of the war, all but 20,000 of acting capital Sievierodonetsk's 130,000 residents had left the city. Shelling of the town of Zolote on Sunday killed at least two people, he added.
Ukraine vows to 'win this war'
Ukrainian Prime Minister Denys Shmyhal said the country was prepared to end the war by diplomacy if possible, but that, "We do not have the intention to surrender".
"We will fight absolutely to the end, to the win, in this war," he told US television.
"Mariupol may be a red line," Mr Shmyhal added.
Ukrainian soldiers resisted a Russian ultimatum to lay down arms in the pulverised port of Mariupol, which Moscow said its forces had almost completely seized in what would be its biggest prize of the nearly two-month war.
Mr Shmyhal said troops there were still fighting, despite a Russian demand to surrender.
"The situation in Mariupol is dire … the city doesn't exist anymore," Mr Kuleba said.
"The remaining Ukrainian army and [a] large group of civilians are basically encircled by the Russian forces. They continue their struggle.
Mr Kuleba said communications with Russian counterparts had been intermittent.
"We didn't really have any contacts with Russian diplomats in recent weeks at the level of foreign ministries," he said.
"The only level of contact is the negotiating team that consists of the representatives of various institutions and members of parliament. They continue their consultations at the expert level but no high-level talks are taking place."
Mr Kuleba said he was expecting "intensification of heavy fighting in eastern Ukraine" in the coming weeks.
Soldiers in steelworks 'well set for defence'
Russia says it has control of residential areas of Mariupol, with some Ukrainian fighters remaining in the Azovstal steelworks, which overlooks the Sea of Azov.
It was not known how many soldiers were in the steelworks. Satellite images have shown smoke and fire coming from the area, which is riddled with tunnels.
Ukrainian President Volodymyr Zelenskyy has said that killing his troops would put paid to peace efforts.
A UK military expert has told the BBC the Ukrainian troops defending the Azovstal steelworks might be able to hold out for some time using guerilla tactics by utilising the building's nuclear bunkers and tunnels.
Justin Crump of security services firm Sibylline said the up-to-800 fighters defending the plant were "really well set for defence", having had almost two months to fortify the site and secure escape routes.
Russia said Ukraine had lost more than 4,000 soldiers in Mariupol as of Saturday.
Kyiv says its total troop losses nationwide so far in the war are less than that, between 2,500 and 3,000. Neither side's figures have been independently verified.
Capturing Mariupol, the main port in the south-eastern region of Donbas, would be a strategic prize for Russia, connecting territory held by pro-Russian separatists in the east with the Crimea region that Moscow annexed in 2014.
After failing to overcome Ukrainian resistance in the north, the Russian military has refocused its ground offensive on the Donbas region, while maintaining long-distance strikes elsewhere including Kyiv.
About four million Ukrainians have fled the country, cities have been shattered and thousands have died since the start of the invasion on February 24.
"The occupiers will be responsible for everything they did in Ukraine," Mr Zelenskyy said on his Telegram account, posting images of destruction he said were akin to the "terrible times" of World War II.
UK politicians barred from Russia
Russia's Foreign Ministry said it had barred entry to the country for Prime Minister Boris Johnson, Foreign Secretary Liz Truss, Defence Secretary Ben Wallace and 10 other British government members and politicians.
The move was taken "in view of the unprecedented hostile action by the British government, in particular, the imposition of sanctions against senior Russian officials", the ministry said in a statement, adding that it would expand the list soon.
The Kremlin has described Mr Johnson, who has been one of Ukraine's staunchest backers, as "the most active participant in the race to be anti-Russian".
A week ago, Mr Johnson visited Kyiv, where he and Mr Zelenskyy praised each other for their cooperation since the Russian invasion.
"The UK and our international partners stand united in condemning the Russian government’s reprehensible actions in Ukraine and calling for the Kremlin to stop the war," a British government spokesperson said in response to Moscow's decision to bar British politicians.
"We remain resolute in our support for Ukraine," the spokesperson added.
ABC/wires
