A wave of Russian missiles have hit cities across Ukraine, officials say.

Kyiv Mayor Vitaly Klitschko said there had been several blasts in the capital, causing at least one death. A hotel has also been damaged.

The attacks happened two days after Russia carried out one of the largest air strikes since the start of the war.

Ukraine President Volodymyr Zelensky had warned Russia could launch more attacks to make Ukrainians "celebrate the New Year in darkness".

Russia has been targeting Ukraine's energy sector in the past few months, destroying power stations and plunging millions into darkness during the country's freezing winter.

Several senior Ukrainian officials have alluded to the strikes in social media posts, saying that Russia would not succeed in ruining their celebrations.

"The occupiers have decided to try to spoil the day for us," Mykolaiv Governor Vitaly Kim said on Facebook.

The head of Ukraine's armed forces, Valerii Zaluzhny, said air defences had shot down 12 of 20 Russian cruise missiles.

In Kyiv, people rushed to shelters as air raid sirens sounded.

Emergency workers were sent to several districts hit by explosions.

Some 20 people were injured in Kyiv, including a Japanese journalist, Mr Klitschko said.

Deputy presidential chief of staff Kyrylo Tymoshenko said on Telegram that a hotel had been damaged.

Air defence has been activated in regions across the country.

In the western city of Khmelnytskyi, a drone attack injured two people, Mr Tymoshenko added.

The attacks came as Russian President Vladimir Putin tried to rally people behind Russian troops fighting in Ukraine, saying the country's future was at stake.

In a combative New Year address surrounded by people in military uniform, Mr Putin said: "We always knew, and today it is confirmed to us yet again, that a sovereign, independent and secure future for Russia depends only on us, on our strength and will."

He presented the invasion of Ukraine's sovereign territory as "defending our people and our historical lands".

But President Zelensky responded with his own message to Russians in Russian.

"Your leader wants to show you that he's leading from the front, and his military is behind him," he said.

"But in fact he is hiding... He's hiding behind you, and he's burning your country and your future. No-one will forgive you for terror."

The Ukrainian government has pleaded with Western leaders to provide it with additional air defences, and US President Joe Biden recently agreed to supply its Patriot system.

The Kremlin rejected Ukraine's suggestion that peace talks could begin in 2023.

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