Russian forces have attacked along a broad front in eastern Ukraine on Tuesday as part of a full-scale ground offensive in the region. 

Ukrainian president Volodymyr Zelensky said the long-awaited "battle for the Donbas" has begun in his evening video address.

Mr Zelensky said a “significant part of the entire Russian army is now concentrated on this offensive”.

The Donbas is Ukraine’s mostly Russian-speaking industrial heartland in the east, where Moscow-backed separatists have been fighting Ukrainian forces for the past eight years and have declared two independent republics that have been recognised by Russia.

In recent weeks, the Kremlin said the capture of the Donbas is its main goal of the war after its attempt to storm Ukraine’s capital Kyiv failed.

“No matter how many Russian troops are driven there, we will fight,” Mr Zelensky vowed. “We will defend ourselves. We will do it every day.”

The stepped-up assaults began on Monday along a front of more than 300 miles, focused on the Donbas regions of Donetsk and Luhansk, with the Russian forces trying to advance in several sections, including from neighbouring Kharkiv.

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In southern Donetsk, Ukraine's General Staff said the Russian military has continued to blockade and shell the strategic port city of Mariupol and fire missiles at other cities.

The Donbas is Ukraine’s mostly Russian-speaking industrial heartland in the east, where Moscow-backed separatists have been fighting Ukrainian forces for the past eight years and have declared two independent republics that have been recognised by Russia.

In recent weeks, the Kremlin said the capture of the Donbas is its main goal of the war after its attempt to storm Ukraine’s capital Kyiv failed.

On Monday morning, Oleksiy Danilov, secretary of Ukraine’s national security council, told Ukrainian media that the defensive line had not been broken.

“Fortunately, our military is holding out,” Mr Danilov said. “They passed through only two cities. This is Kreminna and another small town.”

There were street battles in Kreminna, and Russian forces took control of the city, according to Luhansk regional military administrator Serhiy Haidai. He told Ukrainian TV that heavy artillery fire set seven residential buildings on fire and targeted a sports complex where the nation’s Olympic team trains.

Mr Haidai said that before advancing, Russian forces “just started levelling everything to the ground”. He said his forces retreated to regroup and keep fighting.

In Mariupol, Denys Prokopenko, commander of the Azov Regiment of the Ukrainian National Guard, said in a video message that Russia had begun dropping bunker-buster bombs on the Azovstal steel plant where the regiment was holding out.

The sprawling plant contains a warren of tunnels where both fighters and civilians are sheltering. It is believed to be the last major pocket of resistance in the shattered city.

Russia has Mariupol surrounded and has been fighting a bloody battle to seize it. If Russia takes Mariupol, it would free up troops for use elsewhere in the Donbas, deprive Ukraine of a vital port, and complete a land bridge between Russia and the Crimean Peninsula, seized from Ukraine in 2014.

In western Ukraine near the Polish border, at least seven people were reported killed on Monday in missile strikes.

Lviv has been a haven for civilians fleeing the fighting elsewhere. And to the Kremlin’s increasing anger, the city has also become a major gateway for Nato-supplied weapons.

The attack hit three military infrastructure facilities and an auto shop, according to the region’s governor, Maksym Kozytskyy.

A hotel sheltering Ukrainians who had fled the fighting in other parts of the country was also badly damaged, Lviv Mayor Andriy Sadovyi said.

“The nightmare of war has caught up with us even in Lviv,” said Lyudmila Turchak, who fled with two children from Kharkiv in the east.

Kharkiv, Ukraine’s second-largest city, was hit by shelling that killed at least three people, according to Associated Press journalists on the scene. One of the dead was a woman who appeared to be going out to collect water in the rain. She was found with a water canister and an umbrella by her side.

Moscow said its missiles struck military targets in eastern and central Ukraine including ammunition depots, command headquarters, and groups of troops and vehicles. It reported that its artillery hit hundreds of Ukrainian targets, and that warplanes conducted 108 strikes on troops and military equipment. The claims could not be independently verified.

General Richard Dannatt, a former head of the British Army, told Sky News that Russia was waging a “softening-up” campaign ahead of the Donbas offensive.

A senior US defence official, speaking on condition of anonymity to discuss the Pentagon’s assessments of the war, said there are now 76 Russian combat units, known as battalion tactical groups, in eastern and southern Ukraine, up from 65 last week. That could translate to around 50,000 to 60,000 troops, based on what the Pentagon said at the start of the war was the typical unit strength of 700 to 800 soldiers.