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Russia has started its expected major new offensive in eastern Ukraine, President Zelenskyy has said.
"The Russian troops have begun the battle for the Donbas, for which they have been preparing for a long time," Ukraine's leader said in a video address on Monday night.
"A significant part of the entire Russian army is now concentrated on this offensive."
Russian forces have been repositioning and reinforcing for several weeks after being thwarted in their attempt to capture the capital Kyiv.
"No matter how many Russian troops are driven there, we will fight. We will defend ourselves. We will do it every day," added President Zelenskyy.
The Kremlin has said it wants to "liberate" the region and pro-Russian separatist fighters have been battling Ukraine's military in the area - which includes Donetsk and Luhansk - since 2014.
In other developments:
• Putin says West's "strategy of the economic blitz has failed"
• Zelenskyy submits questionnaire in first step towards obtaining EU membership
• Humanitarian ceasefires "not on horizon" but possible in a few weeks, says UN aid chief
• Images of Russian warship Moskva before it sank emerge online
The president's announcement followed statements by several senior officials that a new stage of the war had begun.
Presidential chief of staff Andriy Yermak wrote on the Telegram messaging app that "the second phase of the war has started" but urged people to stay resolute.
"Believe in our army, it is very strong," he said.
That came after a message from Ukraine's top security official that the "active phase" of a new offensive had started on Monday morning.
Oleksiy Danilov, the security council secretary, said Russia had attempted to break through defences "along almost the entire front line of Donetsk, Luhansk and Kharkiv regions".
There are fears Russia could be more successful than its failed push to take Kyiv.
Former head of the British Army Lord Dannatt told Sky News it would have been "meticulously prepared", as opposed to the "haphazard" attempt to capture the capital.
Mariupol on the brink of falling under Russian control
It comes as the city of Mariupol, which has been pummelled for weeks, appears on the brink of finally coming under total Russian control.
Moscow had given the city an ultimatum: surrender or die - but the last remaining Ukrainian troops ignored the warning and continue to be holed up at the vast Azovstal steel plant.
Upwards of 1,000 civilians have taken refuge in the underground shelters at the plant but Russia continues to bomb the factory, said Mariupol's council.
Bunker-busting bombs are now being dropped, according to the commander of the Azov Regiment of the National Guard.
"Russian occupational forces, and their proxy... know about the civilians, and they keep willingly firing on the factory," said Denys Prokopenk.
Deputy prime minister Iryna Vereshchuk has demanded an "urgent humanitarian corridor" for women, children and civilians.
If Russia takes the city it could free up even more troops for the battle in the east and crucially achieve one of its key aims - creating a land corridor from Crimea, through Mariupol, to Donbas.
Russia's defence ministry also claimed to have hit hundreds of military targets in Ukraine overnight into Monday.
At least seven killed in western city as explosions heard overnight
At least seven people were killed in the western city Lviv, near the Polish border, which has been a relatively safe haven so far and attracted refugees from across the country.
Three military infrastructure facilities that weren't in use were hit, as well as a "barbaric" attack on a civilian service station, said regional governor Maksym Kozytskyy.
Lviv's proximity to Poland and the EU has made it a major gateway for the large amounts of weaponry donated by the US and European allies.
In the early hours of Tuesday morning, Ukrainian media reported a series of explosions along the front line in the eastern Ukrainian city of Donetsk, with shelling taking place in nearby Marinka, Slavyansk, and Kramatorsk.
Local officials also said explosions were heard in Kharkiv in the northeast of Ukraine, Mykolaiv in the south, and Zaporizhzhia in the southeast.
Meanwhile, two British fighters captured in Ukraine have appeared on Russian state TV and asked to be exchanged for pro-Russian politician Viktor Medvedchuk.
It was unclear how freely the two men, Shaun Pinner and Aiden Aslin - were able to talk.
Both spoke separately after being prompted by an unidentified man in footage broadcast on the Rossiya 24 state TV channel.