In what Ukrainian officials are calling a “new phase of the war,” Russian forces attacked along a broad front in eastern Ukraine on Tuesday as part of a full-scale ground offensive. 

Ukraine’s General Staff said Russian forces are focusing their efforts on taking full control of the Donbas region. “The occupiers made an attempt to break through our defenses along nearly the entire frontline,” the General Staff said in a statement early Tuesday.

The stepped-up assaults began 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 the neighboring Kharkiv region.

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.

Britain’s Telegraph newspaper reported Tuesday morning that London is set to send armored missile launchers to Ukraine to support its defense against Moscow.

On Monday night, President Zelensky said in a video address that Russian troops “have begun the battle for the Donbas, for which they have been preparing for a long time,” and 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 Donbas and have declared two independent republics that have been recognized by Russia. Moscow has declared the capture of the Donbas to be its main goal in the war since its attempt to seize the capital, Kyiv, failed.

Troops battled in the streets of Kreminna on Monday before Russia was able to gain control of the city, according to the Luhansk regional military administrator, Serhiy Haidai. Before advancing, Russian forces “just started leveling everything to the ground,” Mr. Haidai said. He said his forces retreated to regroup and keep fighting.

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

“Fortunately, our military is holding out,” Mr. Danilov said.

The Russian military, meanwhile, has made a new demand to the Ukrainian defenders of Mariupol to lay down their arms. Colonel General Mikhail Mizintsev gave the Ukrainian troops holed up at the giant Azovstal steel mill in Mariupol until midday Tuesday to surrender. He said that those who surrender will “keep their lives.”

The commander of the Azov Regiment of the Ukrainian National Guard, Denys Prokopenko, said in a video message earlier that Russia had begun dropping bunker-buster bombs on the steel plant, which 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 from 2014.

In western Ukraine near the Polish border, at least seven people were reported killed Monday in missile strikes on Lviv. The regional governor, Maksym Kozytskyi, said those strikes were launched from planes that came from the direction of the Caspian Sea. The attacks caused the first wartime deaths in Lviv since Russia invaded Ukraine on February 24.

On the diplomatic front, informal talks between Vladimir Putin and the French president, Emmanuel Macron, appear to have broken down. Speaking on French television Monday night, Mr. Macron said, “Since the massacres we have discovered in Bucha and in other towns, the war has taken a different turn, so I did not speak to him again directly since, but I don’t rule out doing so in the future.”