Ukraine has refused to surrender the besieged city of Mariupol in exchange for the safe passage of civilians out of the city.

A deadline for the surrender of the city passed in the early hours of this morning; however, Ukrainian officials had already rejected the proposal out of hand.

Yesterday, Russia said it would allow people to leave the city if they put down their weapons and raised white flags.

Russian Colonel General Mikhail Mizintsev said two corridors would be opened out of the city – one heading east to Russian and another heading west to other parts of Ukraine.

Mariupol authorities were given until the early hours of Monday to decide; however, Ukraine's deputy prime minister and an adviser to Mariupol's mayor both said there would be no surrender.

Deputy Prime Minister Irina Vereshchuk told news outlet Ukrainian Pravda: "There can be no talk of any surrender; laying down of arms. We have already informed the Russian side about this.

"I wrote: 'Instead of wasting time on eight pages of letters, just open the corridor'."

Piotr Andryushchenko, an adviser to Mariupol's mayor, wrote in a Facebook post that he did not need to wait until morning to respond and cursed at the Russians, according to news agency Interfax Ukraine.

Russia has offered few details of what might happen if the deal was rejected; however, the Russian Ministry of Defence has warned the city's authorities they could face a military tribunal if they sided with what it called “bandits”.

At least 2,300 people are believed to have been killed in Mariupol since the Russian invasion began.

The city has been under siege for weeks with air strikes on residential areas and hospitals.

Aid groups have said food, water, and electricity are running low in the city, with humanitarian access limited by the fighting.

The latest air strike hit an art school that was sheltering around 400 people.

Speaking early this morning, Ukraine President Volodymr Zelenskyy said: “They are under the rubble, and we don't know how many survived – but we know that we will certainly shoot down the pilot who dropped that bomb, like about 100 such mass murderers whom we already have downed.”

Meanwhile, emergency services said four people were killed by shelling in the capital city Kyiv on Sunday, with a shopping centre and residential buildings among the places hit.

Kyiv's mayor Vitaliy Klitschko said Ukrainian forces shot down a Russian missile in the city's northwest.

With reporting from IRN