Russian missiles have hit Ukraine's biggest cities, leaving at least five dead and dozens hurt, after Vladimir Putin vowed to intensify attacks.

A woman was killed and 44 others were hurt in the north-eastern city of Kharkiv, according to local officials.

Kyiv Mayor Vitaliy Klitschko said two people died and 49 were wounded in a strike on blocks of flats in the Solomianskyi district of the capital.

Two more deaths were reported in the broader Kyiv region.

There have been major aerial assaults by both sides in recent days.

Russia launched its biggest aerial bombardment of the war late last week, killing more than 40 people. Ukrainian forces responded with an attack on the Russian border city of Belgorod on Saturday, which killed at least 25 people and injured more than 100.

Russia's Vladimir Putin vowed that attack would not go unpunished and Ukraine's President Volodymyr Zelensky said since Sunday alone, Moscow had fired 170 drones and dozens of missiles.

Ukraine's air force said on Tuesday that it had downed 35 drones launched by Russia on Monday night. Russian strategic bombers then followed up the drone strikes with further attacks.

Ukraine's armed forces said after the drone strikes 99 missiles of various kinds had been fired in a repeat of last Friday's onslaught, from sea and air. They said 72 cruise and supersonic missiles had been destroyed.

Poland said it had deployed four F-16 fighter jets to secure its airspace in light of Russia's "long-range aviation activity". Last Friday Poland said an unidentified object, probably a Russian missile, had entered Polish airspace for several minutes before turning back towards Ukraine.

Kyiv officials said debris from Russia's attacks had hit high-rise flats, warehouses and supermarkets, and that two people including an elderly woman had been killed by a missile in the Solomianskyi district to the south-west of the centre.

Hanna, a resident of the building, told the BBC she managed to escape by climbing through her kitchen window after the missile landed outside.

"I want Putin to die very much... and everyone who supports him," she told the BBC. "Because today's event ruined the lives of hundreds, in one minute. There have been a lot of hits before this. A lot killed. All this is on [Putin]. I think he will burn in hell."

Power and water supplies were cut to several areas of the capital and gas pipelines were damaged in one district.

Kharkiv regional governor Oleh Syniehubov said the centre of the city was hit and the air force said it was prepared for further attacks.

The mayor of Mykolaiv, in southern Ukraine, said air defences had brought down drones in the city, with debris causing a fire.

On New Year's Day, six civilians were killed by Russian strikes in various Ukrainian cities.

In a separate development, Russian-installed officials in the occupied city of Donetsk said four people were killed and 13 wounded by Ukrainian shelling on Sunday.

Mr Putin suggested that Western rhetoric towards the war was beginning to change as they started to realise they could not "destroy" Russia.

Ukrainian President Volodymyr Zelensky countered these claims in an interview with The Economist, saying Mr Putin's suggestion that Russia was winning the war was only a "feeling". He highlighted Russia's casualty figures in Ukraine, and said the opposing forces had been unable to take a single large city in 2023.

Mr Zelensky also expressed frustration with Kyiv's Western allies, saying they had lost a sense of urgency.