A massive Russian aerial bombardment that lasted more than 12 hours has killed at least four people and injured 40 others in Ukraine.

Ukrainian President Volodymyr Zelensky said the deaths occurred in the capital, Kyiv, and the victims included a 12-year-old girl.

Russia launched nearly 600 drones and several dozen missiles toward seven regions of Ukraine, its air force said. Zelensky said the "vile" attack also saw at least 16 people injured in the Zaporizhzhia region, including three children.

He warned that Ukraine would retaliate and said the attack showed Moscow "wants to continue fighting and killing". Russia has not yet commented on the latest attack.

Saturday night's extended barrage is one of the heaviest overnight aerial bombardments in recent months as Russia's full-scale invasion of Ukraine continues in its third year.

Zelensky said many of the projectiles were aimed at Kyiv, where the Institute of Cardiology had been damaged.

A large bakery, an automobile rubber factory, as well as apartment buildings and civilian infrastructure were also targeted, he said.

Zelensky said that Zaporizhzhia, Khmelnytskyi, Sumy, Mykolaiv, Chernihiv, and Odesa regions were also hit. Sumy's regional governor said a 59-year-old man had died in strikes in the past day.

Zaporizhzhia's Governor Ivan Fedorov said the three children who were injured included two boys, aged 11 and 12, and a nine-year-old girl.

One boy was caught in an explosion while the other had suffered carbon monoxide poisoning, he said. Both are in a serious condition.

Zelensky vowed that Ukraine "will strike back" in a bid to "force diplomacy" from Russia, and said he was counting on a "strong reaction" from Europe and the United States.

"This dastardly attack took place in fact as the end of the week of the UN General Assembly, and this is how Russia declares its real position," he said.

Zelensky reiterated his support of US President Donald Trump's threat of harsher sanctions on Russia, as well as his call for European allies to curb their Russian oil and gas imports.

Trump has recently shifted his position on the war, saying for the first time last week that he thought Ukraine could retake the land it had lost from Moscow as the Russian economy flagged under the strain of a prolonged war.

The US president has so far desisted from imposing further sanctions on Russia, but has appeared increasingly frustrated with the lack of eagerness from the Kremlin to begin peace talks.

Zelensky warned on Saturday that Russia would not stop with his country - which is why it was testing European air defences with the recent incursions in several countries belonging to the Nato military alliance.

Meanwhile, jets were scrambled in neighbouring Poland early on Sunday as Russia hit western Ukraine, the nation's armed forces said.

The Polish military further described the actions - which have become routine since Polish and Nato aircraft shot down three Russian drones in Poland's airspace on 10 September - as preventative.

Earlier this week, Moscow denied responsibility after Denmark said drones were flown over its airports. Denmark itself has said the incidents appeared to be the work of a "professional actor", without specifying who this may be.

Estonia and Romania have also accused Russia of violating their airspace.

After the incursions, Nato launched a mission to bolster its eastern flank.

Trump has gone as far as to say that Nato nations should shoot down Russian planes in their airspace.

In a speech to the UN General Assembly on Saturday, Russia's Foreign Minister Sergei Lavrov said his country had no intention of attacking EU or Nato member states - but warned of a "decisive response" to any "aggression" directed towards Moscow.