As Moscow launches a "new phase of the war" in Ukraine, Russian forces are intensifying their offensive against Ukraine's entire eastern front on Tuesday as part of a full-scale ground offensive to take control of the country's eastern industrial heartland.

Russia launched its long-awaited all-out assault on eastern Ukraine, unleashing thousands of troops in what Ukraine described as the "Battle of Donbass," a campaign to seize two provinces and salvage a battlefield victory.

Ukrainian officials insisted their troops would withstand the new assault, which they said began overnight with massive Russian artillery and rocket barrages and attempts to advance across almost the entire stretch of the eastern front.

Ukraine's general staff said Russian forces are focusing their efforts on taking full control of the Donbass region. "The occupiers made an attempt to break through our defenses along nearly the entire front line," the general staff said in a statement early Tuesday.

In southern Donetsk, the general staff said the Russian military has continued to blockade and shell the strategic port city of Mariupol and fire missiles at other cities.

Russian Foreign Minister Sergey Lavrov also confirmed Moscow was starting a new stage of what it calls its "special military operation" in Ukraine. "Another stage of this operation (in eastern Ukraine) is beginning and I am sure this will be a very important moment of this entire special operation," Lavrov said in an interview with the India Today TV channel.

Russian forces have seized the city of Kreminna in eastern Ukraine and Ukrainian troops have withdrawn from the city, the regional governor said.

Kreminna, a city of more than 18,000 people about 100 kilometers (62 miles) southeast of the capital Kyiv, appears to be the first city captured in a new Russian offensive in eastern Ukraine.

"Our defenders had to withdraw. They have entrenched themselves in new positions and continue to fight the Russian army," Serhiy Gaidai, the governor of the Luhansk region, told a briefing.

He said Russian forces had attacked "from all sides." "It is impossible to calculate the number of dead among the civilian population. We have official statistics – about 200 dead – but in reality, there are many more," he said, without making clear what period the estimated death toll covered.

Russia has issued another ultimatum to Ukrainian fighters trapped in a steel plant because of the "catastrophic situation" in the embattled city of Mariupol. The Russian Defense Ministry offered on Tuesday the Ukrainian military in Ukraine's Mariupol city to surrender, according to the ministry's spokesperson.

Speaking at a press briefing in Moscow, Igor Konashenkov said Moscow offers the Ukrainian soldiers to announce a cease-fire at noon local time (9 a.m. GMT), then organize a communication channel, open a safe passage at 2 p.m. Moscow time (11 a.m. GMT) for the exit of the soldiers without weapons, which will be open until 4 p.m. (1 p.m. GMT).

'No safe corridors'

Meanwhile, Ukraine was for the third successive day unable to secure Russia's agreement to establish any humanitarian corridors to evacuate civilians trapped in cities and towns, Deputy Prime Minister Iryna Vereshchuk said Tuesday.

"Today, April 19, unfortunately, there are no humanitarian corridors," Vereshchuk wrote on Facebook, adding that intensive shelling continued in the Donbass region of eastern Ukraine.

"According to Mariupol: (The) Russians refuse to provide a corridor for the exit of civilians in the direction of Berdyansk," Vereshchuk said.

She said "difficult negotiations" were taking place to try to arrange humanitarian corridors in the southern region of Kherson and in the Kharkiv region of eastern Ukraine.

On Monday, Ukrainian President Volodymyr Zelenskyy said in a video address that a "significant part of the entire Russian army is now concentrated on this offensive."

Moscow-backed separatists have been fighting Ukrainian forces for eight years in the mostly Russian-speaking Donbass and have declared two independent republics that have been recognized by Russia. Russia has declared the capture of Donbass to be its main goal in the war since its attempt to seize the capital, Kyiv, failed.

"No matter how many Russian troops are driven there, we will fight," Zelenskyy vowed. "We will defend ourselves."

The breakthrough at Kreminna brings the Russians closer to the city of Slovyansk, which is seen as a key target in the Russian offensive. Slovyansk was seized by pro-Russian fighters in 2014, only to be retaken by Ukrainian forces months later following intense fighting.

Russian troops have already seized the city of Izyum, which sits along a highway north of Slovyansk, and they are poised to push toward the city from the north and the east. Slovyansk lies just north of another key city, Kramatorsk, where an earlier Russian attack on a train station killed more than 50 people.

On Monday morning, Oleksiy Danilov, secretary of Ukraine’s national security council, told Ukrainian media that the defensive line had not been broken elsewhere. "Fortunately, our military is holding out," Danilov said.

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 Donbass, deprive Ukraine of a vital port and complete a land bridge between Russia and the Crimean Peninsula, seized from Ukraine from 2014.

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

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 airstrikes on troops and military equipment. The claims could not be independently verified.

A senior U.S. defense 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.