Kyiv, Ukraine - Russia fired a wave of attack drones and missiles at Ukraine that killed at least four people, authorities said Tuesday, after a second night of heavy strikes across the war-battered nation.

Within hours of the barrage, Ukraine claimed fresh advances in its surprise assault on Russia's Kursk border region and reported taking nearly 600 Russian troops as prisoners in the past three weeks.

"Crimes against humanity cannot be committed with impunity," President Volodymyr Zelensky said in a post on social media, reporting on Tuesday four killed and 16 wounded.

AFP journalists in the capital Kyiv heard air raid sirens echo over the city throughout the night as well as an explosion, likely from air defence systems.

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Monday's attack was one of Moscow's largest-ever on Ukraine, prompting Kyiv to push for allies' permission to use Western-provided weapons to strike deep inside Russia.

Local authorities said earlier that two people had been killed in the southeastern Zaporizhzhia region and two in the central city of Kryvyi Rig after a missile struck a hotel.

The hotel strike comes just days after a team working for the Reuters news agency was hit by a missile in their hotel in the eastern Ukrainian city of Kramatorsk, killing a safety advisor working with the agency.

The Russian attacks on Monday triggered widespread blackouts and spurred condemnation from Ukraine's allies in Europe and the US.

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Russia said the attack had targeted infrastructure linked to the Ukrainian military. NATO member Poland said its airspace was violated during the barrage, probably by a drone.

Since invading in February 2022, Russia has launched repeated large-scale drone and missile attacks on Ukraine, including punishing strikes on energy facilities.

Ukraine's electricity grid operator said Tuesday that emergency blackouts would be applied throughout the day to reduce pressure on the grid following the fresh attacks that damaged energy infrastructure nationwide.

Local Ukrainian authorities said separately that three civilians had been killed in the Dnipropetrovsk, Kharkiv, and Kherson regions in Russian drone and artillery attacks.

Ukrainian forces have been pushing their offensive in Kursk, a surprise operation that has seen Kyiv gain swathes of territory in three weeks.

The governor of Russia's Belgorod region, which borders Kursk and Ukraine, said Tuesday he was aware of reports that the Ukrainian army had tried to cross the border.

"Information has emerged that the enemy is trying to break through the border of the Belgorod region," its governor Vyacheslav Gladkov said.

"According to the Russian defense ministry, the situation on the border remains difficult but under control," he said on social media.

Zelensky said late Monday that Ukraine's cross-border incursion launched on August 6 was partially to "compensate" for Kyiv's inability to strike deeper into Russian territory.

He has been appealing to Ukraine's allies to allow his forces to use Western-supplied weapons to strike targets inside Russian territory as part of efforts to thwart more aerial bombardments.

Ukraine's army chief Oleksandr Syrsky said his forces had made fresh gains in Kursk recently and now controlled 100 towns and villages across almost 500 square miles.

He also claimed that Russian forces had redeployed some 30,000 troops to help fend off the Kursk incursion, and said Ukraine had taken 594 POWs in the weeks of the incursion – the first time Kyiv has offered a precise figure.

Moscow has nonetheless been making steady gains in Ukraine and said Tuesday that its forces had captured the village of Orlivka near the strategic railway hub of Pokrovsk.

Zelensky had said late Monday that defending Pokrovsk was "difficult" and that Ukraine was strengthening its positions there as Russian forces advance.

This week, AFP journalists saw civilians evacuating by train from Pokrovsk, once home to around 60,000 people, with panicked residents carrying their belongings in bags and pets with them.