Russia has launched an assault on cities and villages along a hundreds-kilometer-long boomerang-shaped front, sending additional troops into Ukraine in a potentially decisive battle for control of the country's eastern industrial heartland.

If successful, Russia's invasion of what is known as the Donbas region will effectively divide Ukraine in half.

It would provide Russian President Vladimir Putin with a much-needed triumph following Moscow's failed attempt to seize the Ukrainian capital of Kyiv and higher-than-expected losses nearly two months into the war.

Kharkiv and Kramatorsk were targeted, while Russia reportedly claimed missile strikes on regions west of the Donbas around Zaporizhzhia and Dnipro.

Major General Igor Konashenkov, spokesman for the Russian Defense Ministry, air-launched missiles damaged 13 Ukrainian personnel and weapon positions. At the same time, the air force hit 60 additional Ukrainian military targets, including missile warhead storage depots.

Over the last 24 hours, Russian artillery has struck approximately 1300 Ukrainian military structures and over 1200 troop concentrations, he claimed. Independent verification of the assertions was not possible.

On Monday, the Russian assault began along a front spanning more than 480 kilometers from north-eastern Ukraine to the country's southeast, in what both sides termed a new chapter of the war.

Russian forces attempted to "breakthrough our defenses along nearly the entire front line."

Several weeks ago, following Russia's failed attempt to seize Kyiv, the Kremlin announced its primary objective to be the conquest of the predominantly Russian-speaking Donbas, where Moscow-backed rebels have been fighting Ukrainian forces for eight years.

A Russian triumph in the Donbas would deprive Ukraine of industrial assets, including mining, metals plants, and factories manufacturing heavy equipment.

According to a senior US defense source speaking on anonymity to discuss the Pentagon's assessment of the battle, the Russians added two more combat units, known as battalion tactical groups, to Ukraine in the past 24 hours.

This increased the country's total number of units to 78, all located in the south and east, up from 65 last week, the official added.

This equates to around 55,000 to 62,000 troops, based on the Pentagon's stated typical unit strength of 700 to 800 soldiers at the outset of the war. However, assessing Russia's combat capability accurately at this stage is challenging.

Similarly, a European diplomat, speaking on anonymity to discuss military assessments, stated that Russia had between 10,000 and 20,000 foreign fighters in the Donbas.

According to the official, they are a combination of mercenaries from Russia's private Wagner Group and Russian proxy soldiers from Syria and Libya.

While Ukraine described Monday's attacks as the commencement of a long-awaited offensive in the east, several analysts noted that an escalation has been underway and questioned whether this was genuinely the start of a new offensive.

According to the US official, the operation in the Donbas has begun in a limited fashion, namely in a region south of Donetsk and south of Izyum.

Justin Crump, a former British tank commander who now works for the strategic advising firm Sibylline, believes the Ukrainian remarks could be part of an attempt to get allies to deploy different weapons.

"What they're trying to do by positioning this, I think, is... focus people's minds and effort by saying, 'look, the conflict has begun in the Donbas,'" Mr. Crump explained.

"This puts some pressure on NATO and EU suppliers to declare, 'Guys, we're going to start fighting now. We require this immediately.'"

Arms from Europe and America have been critical in helping the outgunned Ukrainians to repel the Russians.

On Tuesday, Dutch Prime Minister Mark Rutte informed Ukrainian President Volodymyr Zelenskyy of the Netherlands' intention to deliver "heavier material," including armored vehicles.

According to Associated Press journalists in Kharkiv, at least four people were killed and three injured in a Russian attack on a residential part of the city. Residents try to maintain a sense of normalcy by growing spring flowers in public spaces.

According to AP journalists on the scene, Kramatorsk was also shaken by an explosion, which killed at least one person and injured three others.

Eyewitness stories and government sources have painted a broad image of the Russian advance. However, independent reporting in areas of the Donbas controlled by Russian forces and separatists is highly restricted, making it difficult to ascertain what is happening on the ground in many locations.

According to military analysts, the Russians' objective is to encircle Ukrainian forces from the north, south, and east.

The campaign's centerpiece is the capture of Mariupol, the now-devastated Donbas city that the Russians have surrounded since the war's inception.

Mariupol's capture would deprive Ukraine of a critical port and would complete a land bridge between Russia and the Crimean Peninsula, which Russia annexed from Ukraine in 2014.

Additionally, it would free up Russian troops for deployment elsewhere in the Donbas.

According to Russian estimates, a few thousand Ukrainian troops remained holed up in a vast Mariupol steel complex, forming what was believed to be the city's last significant pocket of resistance.

On Tuesday, Russia issued a new surrender ultimatum to Ukrainian defenders, stating that those who surrender will "keep their lives," and declaring a cease-fire in the area to allow militants to exit the plant.

The Ukrainians have previously rejected similar proposals, and there was no immediate confirmation of a cease-fire.

On a messaging app, Ramzan Kadyrov, Chechnya's Kremlin-backed leader, said that Russian forces would root out Ukrainian resistance within hours and take complete control of the steel mill on Tuesday.

Mr. Kadyrov is well-known for his bravado and has previously forecast the city's demise.