(Adds comment by Zelenskiy, updates dateline)
* Russia tells Ukrainian fighters in steelworks to lay down arms
* Bombardments continue elsewhere around Ukraine
* Ukrainian President Zelenskiy says occupiers must pay
* Pope decries 'cruel and senseless' conflict
By Oleksandr Kozhukhar and Alessandra Prentice
LVIV/KYIV, April 17 (Reuters) - Ukrainian soldiers resisted a Russian ultimatum to lay down arms on Sunday 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.
Ukrainian Prime Minister Denys Shmyhal said troops in Mariupol were still fighting despite a Russian demand to surrender by dawn.
"The city still has not fallen," he told ABC's "This Week" programme, adding that Ukrainian soldiers continue to control some parts of the southeastern Ukrainian city.
Russia said on Saturday it had control of urban areas, with some Ukrainian fighters remaining in the Azovstal steelworks overlooking the Sea of Azov.
Capturing Mariupol, the main port in the Donbas region, 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 Donbas while launching long-distance strikes at targets elsewhere including the capital, Kyiv.
About four million Ukrainians have fled the country, cities have been shattered and thousands have died since the start of the invasion on Feb. 24.
The economic damage is significant too - Shmyhal said Ukraine's budget deficit was around $5 billion a month and called for Western governments to provide more financial aid.
President Volodymyr Zelenskiy said on Twitter he had discussed ensuring Ukraine's financial stability and preparations for post-war reconstruction with International Monetary Fund Managing Director Kristalina Georgieva. She replied that support was "essential to lay the foundations for rebuilding a modern competitive #Ukraine."
Earlier, he posted on his Telegram account images of destruction he said were akin to World War Two.
"The occupiers will be responsible for everything they did in Ukraine," Zelenskiy said.
'CRUEL AND SENSELESS WAR'
Implicitly criticizing Russia, Pope Francis pleaded for an end to the bloodshed and lamented the "Easter of war" during his address in St. Peter's Square after Mass.
"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.
Zelenskiy accused Russia on Saturday of "deliberately trying to destroy everyone" in Mariupol.
The Azovstal steelworks, one of Europe's biggest metallurgical plants with a maze of rail tracks, tunnels and blast furnaces, has become a last stand for the city's outnumbered defenders.
"All who lay down their arms are guaranteed that their lives will be spared," Russia's Defence Ministry said on Saturday.
It was not known how many soldiers were in the steelworks. Satellite images have shown smoke and fire coming from the area. Zelenskiy has said killing his troops would put an end to peace efforts.
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. Reuters has not been able to verify either side's figures.
Russia calls its action a special military operation to demilitarise Ukraine and eradicate what it calls dangerous nationalists. The West and Kyiv accuse Russian President Vladimir Putin of unprovoked aggression.
A representative in Mariupol of the Azov forces – a one-time far-right militia now part of Ukraine's National Guard whose destruction is among Moscow's war objectives – said international intervention was needed to help civilians, including children, sheltering at the steelworks.
"There are civilians at Azovstal who are afraid of Russia's guarantees for their exit," the Azov representative said in a message to Reuters.
Reuters has not been able to verify whether there are significant numbers of civilians at the plant.
There have been on-off negotiations between Ukraine and Russia since the start of the war.
Ukrainian Foreign Minister Dmytro Kuleba said in a CBS News interview on Sunday that the situation in Mariupol was "dire" and could be a "red line" in the path of negotiations.
Elsewhere in Ukraine, there were more reports on Sunday of Russian strikes around major population centres.
Local media reported an explosion in Kyiv, though 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, according to the RIA news agency.
Shelling in Ukraine's second biggest city, Kharkiv, killed five people and injured 13, Ukrainian public broadcaster Suspilne reported. A Reuters correspondent in Kharkiv heard multiple explosions in quick succession and saw debris from missiles.
"This is nothing but deliberate terror: mortars, artillery against ordinary residential quarters, against ordinary civilians," Zelenskiy said in his nightly video address.
As cleanup 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. The State Emergencies Service 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. "We have survived these horrors and we are constantly crying."
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.
On Sunday, police in Donetsk region said that over the past 24 hours Russian forces opened fire on 13 settlements under Ukrainian control, killing two civilians.
(Reporting by Reuters journalists in Kyiv and Lviv; and Reuters bureaus worldwide; Writing by Andrew Cawthorne and Michael Martina; Editing by Nick Macfie, Frances Kerry, Helen Popper, Grant McCool and Daniel Wallis)