Ukraine has said it will “fight absolutely to the end” as the last-known pocket of resistance in Mariupol hopes to defend the city against Russian forces.

Prime Minister Denys Shmyhal said Ukraine’s soldiers will keep fighting in the besieged port city, which has been reduced to rubble in a seven-week siege, as Russian missiles and rockets also battered other parts of the country.

The city of Mariupol appears to be on the brink of falling in what would give Moscow its biggest victory of the war so far.

Six dead after Russia bombs Lviv – live Ukraine updates

Russian troops would then be freed up for the expected new offensive to take control of the Donbas region in the east of Ukraine.

It also would allow Russia to fully secure a land corridor to the Crimean Peninsula, which it seized from Ukraine in 2014, and deprive the country of a major port and its prized industrial assets.

Mariupol’s last pocket of resistance is made up of a few thousand fighters who are in a four-square mile sprawling steel plant laced with tunnels.

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Many civilians, including children, are also sheltering at the Azovstal plant, the head of the city’s patrol police has told local television.

The soldiers and civilians are holed up as there appears to be little hope of a military rescue by Ukrainian forces anytime soon.

Vladimir Putin’s military gave the city’s defenders a surrender-or-die ultimatum with a midday deadline on Sunday, saying those who laid down their arms were “guaranteed to keep their lives”.

But Ukrainian fighters ignored it, just as they rejected previous ultimatums.

“We will fight absolutely to the end, to the win, in this war,” Mr Shmyhal vowed on Sunday.

He said Ukraine is prepared to end the war through diplomacy if possible “but we do not have intention to surrender”.

In other developments:
• Six reported killed in missile strikes on western city of Lviv – where Ukrainians have been fleeing to seek safety
• Ukraine “may have to accept loss of territory” – military expert says
• Pope Francis marked an “Easter of war” in an address from St Peter’s Square
• Austrian chancellor says Vladimir Putin believes he is winning the war

Ukraine’s foreign minister, Dmytro Kuleba, has said the “dire” situation in Mariupol may be a “red line” in the path of negotiations.

The relentless bombardment and street fighting there has left 21,000 people dead, according to Ukrainian estimates.

Meanwhile, witnesses reported multiple explosions in the city of Lviv early on Monday.

Lviv and the rest of western Ukraine have been less affected by the fighting than other parts of the country, and the city was considered to be a relatively safe haven.

The city’s mayor, Andriy Sadovyi, said that five missiles struck the city and that emergency services were responding.

Russia has also carried out aerial attacks near the capital Kyiv and elsewhere in an apparent effort to weaken Ukraine’s military capacity ahead of the anticipated assault on Donbas.

After the humiliating sinking of the flagship of Russia’s Black Sea Fleet last week in what the Ukrainians boasted was a missile attack, the Kremlin has vowed to step up strikes on the capital.

Russia said on Sunday that it had attacked an ammunition plant near Kyiv overnight with precision-guided missiles, the third such strike in as many days.

Explosions were also reported in Kramatorsk, the eastern city where rockets killed at least 57 people at a train station earlier this month.

Ukrainian President Volodymyr Zelenskyy used his nightly address to the nation to say Russian troops in southern Ukraine have been carrying out torture and kidnappings as he called on the world to respond.

“Torture chambers are built there,” Mr Zelenskyy.

“They abduct representatives of local governments and anyone deemed visible to local communities.”

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The president also said the theft of humanitarian aid has caused famine.

He added Mr Putin’s forces are creating separatist states and introducing Russian currency in parts of the Kherson and Zaporizhzhia regions.

Intensified Russian shelling of Ukraine’s second-largest city, Kharkiv, has killed 18 people and wounded 106 in the last four days alone, Mr Zelenskyy added.

“This is nothing but deliberate terror. Mortars, artillery against ordinary residential neighbourhoods, against ordinary civilians,” he said.

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The Ukrainian president also said a planned Russian offensive in eastern Ukraine “will begin in the near future.”

Mr Zelenskyy again called for increased sanctions against Russia, including its entire banking sector and oil industry.

“Everyone in Europe and America already sees Russia openly using energy to destabilize Western societies,” he said.

“All of this requires greater speed from Western countries in preparing a new, powerful package of sanctions.”

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