“The Russian troops have begun the battle for the Donbas, which they have been preparing for a long time,” the Ukrainian leader said in a video address Monday night.
“A significant part of the entire Russian army is now concentrating on this offensive.”
Russian troops have been repositioning and reinforcing for several weeks after being thwarted in their attempts to capture the capital Kiev.
“It does not matter how many Russian troops are driven there, we will fight. We will defend ourselves. We will do it every day,” added President Zelenskyy.
Ukraine news live: Russia drops ‘bunker-buster’ on Mariupol
The Kremlin has said it wants to “liberate” the region and since 2014 pro-Russian separatist fighters have been fighting Ukraine’s military in the area – which includes Donetsk and Luhansk.
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• Images of the Russian warship Moscow before the sinking appear online
The president’s announcement followed statements by several senior officials that a new stage of the war had begun.
President Andriy Yermak wrote on the Telegram messaging app that “the second phase of the war has begun”, but urged people to remain 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 Monday morning had begun.
There are fears that Russia may be more successful than its failed pressure to take Kiev.
Former British Army Chief of Staff Lord Dannatt told Sky News it would be “surf-ready”, as opposed to the “haphazard” attempt to capture the capital.
Mariupol on the verge of falling under Russian control
This is because the city of Mariupol, which has been pummeled for weeks, appears on the verge of eventually 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 remained in the large Azov steel factory.
More than 1,000 civilians have taken refuge in the underground shelters near the plant, but Russia continues to bomb the factory, the Mariupol council said.
Bunker-busting bombs are now dropped, according to the commander of the Azov Regiment of the National Guard.
“Russian occupying forces, and their proxies … know about the civilians, and they remain willing to shoot at the factory,” said Denys Prokopenk.
Deputy Prime Minister Iryna Vereshchuk has demanded an “urgent humanitarian corridor” for women, children and citizens.
If Russia takes the city, it could free up even more troops for the battle in the east and crucially achieve one of its main goals – to create a land corridor from the Crimea, via Mariupol, to Donbas.
The Russian Ministry of Defense also claimed that it had hit hundreds of military targets in Ukraine by Monday night.
At least seven people were killed and hundreds more injured in what became known as the Nightmare
At least seven people have been killed in the western city of Lviv, near the Polish border, which until now has been a relatively safe haven and has attracted refugees from all over the country.
Three military infrastructure facilities that were not in use were hit, such as a “barbaric” attack on a civilian service station, said regional governor Maksym Kozytskyy.
Lviv’s close to Poland and the EU has made it an important gateway to the large quantities of weapons donated by American 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, during which bombings took place near Marinka, Slavyansk and Kramatorsk.
Local officials also said explosions were heard in Kharkiv in northeastern Ukraine, Mykolaiv in the south, and Zaporizhzhia in the southeast.
Meanwhile two British fighters caught in Ukraine have appeared on Russian state TV and asked to be traded for pro-Russian politician Viktor Medvedchuk.
It was unclear how freely the two men, Shaun Pinner and Aiden Aslin – could talk.
Both spoke separately after being questioned by an unknown man in images broadcast on the Rossiya 24 state TV channel.
