Russian and Ukrainian forces clashed on Tuesday along the eastern front line, after Mr. Zelensky said the battle for the Donbas had begun.

Ukraine’s top security official, Oleksiy Danilov, said Russia was trying breakthrough Ukrainian defensive positions throughout Ukraine’s east.

The offensive had been expected after Russia failed to seize Kyiv.

After its push to overrun the capital stalled, Moscow announced its military would focus instead on eastern Ukraine where Russian-backed separatists have been fighting Ukrainian forces since 2014.

Luhansk is one of the most fiercely contested regions, and on Tuesday its Governor Serhiy Hayday said it had come under attack from all sides.

“They moved in but our defenders had to retreat,” Mr. Hayday said. “The enemy was shelling every meter of our defence line.”

The strategic port city of Mariupol, meanwhile, has come under intense bombardment.

Ukraine says civilians and children are among those holed up in the complex, but pro-Russian officials in the city have disputed this.

Mariupol is a key Russian target that if captured would allow its troops to complete a land bridge between the occupied Crimean peninsula and separatist-held regions of eastern Ukraine.

In Kharkiv, which is 400km (249 miles) away in Ukraine’s northeast, officials said three people had been killed and 21 injured in a new wave of attacks on the city.

“The intensity of the shelling of Kharkiv has increased,” the regional governor Oleg Sinegubov said in a post on Telegram.

Russia initially appeared to want to capture major Ukrainian cities and topple the country’s government.

But after facing stiff resistance, Russian defence officials said that its main objectives in the “first stage of the operation” had been “generally accomplished” and its forces were moved from areas around the capital.

They announced plans to redirect the focus of the invasion towards the “liberation” of the mostly Russian-speaking Donbas region.

Russia’s President Vladmir Putin has portrayed the invasion as an attempt to demilitarise and “denazify” Ukraine, something Ukraine and its allies dismiss as a ruse for an unprovoked attack.

Russian defence officials said its forces struck more than 1,200 targets in Ukraine on Monday night, including 25 military command posts in Mykolayiv and Kirovsk as well as two weapon depots in east Ukraine.

Describing the fresh offensive in a television interview, Moscow’s Foreign Minister Sergei Lavrov said “another stage of this operation is beginning, and I’m sure this will be a very important moment.”

Speaking in a video message on Monday night, Mr. Zelensky said that his forces had pledged to “not give up anything Ukrainian”.

“A very large part of the entire Russian army is now focused on this offensive,” he added, but said that Ukraine’s forces will fight on “no matter how many Russian troops are driven there, we will fight”.

Moscow claimed last month that it controlled 93% of Luhansk and 54% of Donetsk and its forces are expected to try and encircle the remaining Ukrainian troops in the region.

But they face a protracted fight with some of Kyiv’s most battle-hardened troops. Ukraine is believed to have between 40-50,000 soldiers in the Donbas, many of whom have spent years fighting against Russian-backed separatists forces in the region.

The change in Russia’s objectives as set out by President Vladimir Putin during a speech last week, where he announced that his aim was “to help the people who live in the Donbas, who feel their unbreakable bond with Russia”.

The Pentagon’s press secretary, John Kirby, cautioned Russia could be “setting the conditions for future offensive operations” and officials in Kyiv warned that the new Russian offensive does not mean that Moscow has ended its attacks on other parts of Ukraine.

“Putin hasn’t removed the goal to destroy us as a state and our political leadership,” Mr. Danilov said in an interview with Ukrainian TV.