Updated April 19, 2022 at 2:01 PM ET

Ukrainians had been expecting a renewed Russian offensive in the eastern region known as the Donbas, and now Ukraine's president says it's underway.

President Volodymyr Zelenskyy said in his evening address that Russian forces have begun their new offensive against cities in the east and south, adding that a "substantial part" of the Russian army is now taking part in the military operation.

"Today we can already say that Russian armed forces have begun the assault on the Donbas, which it has been preparing for," Zelenskyy said.

A senior U.S. defense official said on Tuesday that Russia is conducting "limited offensive operations" southwest of Donetsk and south of Izium, which are a "prelude to larger offensive operations."

Russia has had its eye on Donbas for years

The Donbas region in eastern Ukraine along the border with Russia has long been of interest to the Kremlin.

In 2014, after antigovernment protests broke out across Ukraine, two breakaway regions in Donbas formed under the control of Russian-backed separatists: the Luhansk People's Republic and the Donetsk People's Republic.

Those two regions comprised parts of the larger Luhansk and Donetsk provinces that make up the Donbas.

Russia denied sending any forces into Donbas to bolster the insurgency in the intervening years, but that claim is disputed.

Just before the invasion of Ukraine, Russian President Vladimir Putin officially recognized the separatist republics, where forces loyal to the Kremlin had been in an intense standoff with the Ukrainian military.

Putin then used the unrest in Donbas as a pretext for the wider invasion of the country, saying without any evidence that he was protecting people in the region from genocide by the Ukrainian government.

There's some dispute over whether Russia's new offensive has started

"The battle for #Donbas has begun," Melinda Simmons, the British ambassador to Ukraine, said in a tweet.

"Big battle for Donbas has started," Ukrainian lawmaker Inna Sovsun tweeted.

But others haven't been so definitive that the anticipated assault has commenced in earnest. The Pentagon says Russia is still conducting "shaping operations," or laying groundwork for the offensive by sending in more battalions, artillery, bombs and missiles.

Meanwhile, a large portion of the Ukrainian army is already in place, and will soon be getting a lot more heavy weaponry from the U.S. and NATO in the form of artillery, helicopters, drones and armored vehicles.

Russian rockets and artillery shells fell on multiple Ukrainian cities Tuesday, with Ukrainian media reporting explosions and air raid sirens across hundreds of miles.

Strikes hit targets in the far west of Ukraine, but most reports of attacks came from the eastern part of the country, including in the second-largest city of Kharkiv.

How the new assault could play out

Russian troops will likely try to box in the Ukrainians, but it's unclear whether they have enough combat power and competence to do so in the days and weeks ahead.

In the southeastern port city of Mariupol, for example, Russian troops have sieged, bombarded and starved the city but failed to take control of it, due in part to missteps by Russian forces and their commanders.

Urban warfare favors the defenders and Russia's destruction of the city has given Ukrainian fighters even more advantages, according to the intelligence firm Janes. Ukrainians also have "the will to fight," retired U.S. Army officer John Spencer said, while the Russians do not.

The Russians have about 75% of their combat power from the start of the invasion, a senior U.S. defense official said. The Russian military outnumbers Ukrainian forces, but the Ukrainians "still have a lot of combat power" and are getting "resupplied every single day," the official added.

Russia has sent in 12 battalion tactical groups, each numbering 800 to 1,000 soldiers. But Fred Kagan, an American Enterprise Institute analyst, says those numbers alone don't tell the full story. Many battalions are weak because of casualties and lost and damaged equipment, and they have poorly trained conscript forces who will face a "battle-hardened" Ukrainian army, Kagan noted.

Mariupol is valuable because it's a key port, and it would also help the Russians build a land bridge from Russia along the coast to Crimea, which it annexed in 2014. If Mariupol were to fall, the Pentagon says most of the Russian troops there would head north to the Donbas region for a major battle.

Even in that case, Russian forces would still face fighting in cities across the northeast and south as the Ukrainians continue to put up a fierce resistance.

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