KYIV, Ukraine >> Russia hurled its military might against Ukrainian cities and towns and poured more troops into the war, seeking to slice the country in two in a potentially pivotal battle for control of the eastern industrial heartland of coal mines and factories.

The fighting unfolded along a boomerang-shaped front hundreds of miles long in what is known as the Donbas. If successful, it would give President Vladimir Putin a victory following the failed attempt by Moscow’s forces to storm the capital, Kyiv, and heavier-than-expected casualties.

In Mariupol, the devastated port city in the Donbas, Ukrainian troops said the Russian military dropped heavy bombs to flatten what was left of a sprawling steel plant — believed to be the defenders’ last holdout — and hit a hospital where hundreds were staying.

The Ukrainian General Staff said Wednesday that Russia was continuing to mount offensives at various locations in the east as its forces probe for weak points in the Ukrainian lines. The General Staff said in a statement that defeating the last resistance in the Azovstal steel mill in Mariupol remains Russia’s top priority.

Deputy Prime Minister Iryna Vereshchuk said that there was a “preliminary” agreement to open a humanitarian corridor for women, children and the elderly to leave Mariupol west to the Ukraine-controlled city of Zaporizhzhia on Wednesday afternoon.

She said on the the messaging app Telegram that civilians in Mariupol were facing a “catastrophic humanitarian situation.”

Vereshchuk previously said no agreement had been reached with Russia on an evacuation route on each of the past three days. There was no immediate confirmation from the Russian side, which issued a new ultimatum to the Ukrainian defenders to surrender Wednesday after a previous ultimatum was ignored.

The Russian Defense Ministry said those who surrender will be allowed to live and given medical treatment. The Ukrainian troops have repeatedly vowed not to give up.

Ukraine and Russia have frequently blamed each other for obstructing evacuations from Mariupol or firing along the agreed route, which has typically only been open to people traveling using private vehicles.

Key to the Russian campaign is the capture of Mariupol, which would deprive Ukraine of a vital port and complete a land bridge between Russia and the Crimean Peninsula, seized from Ukraine in 2014. It would also free up Russian troops to move elsewhere in the Donbas.

A few thousand Ukrainian troops, by the Russians’ estimate, remained holed up in the sprawling steel plant.

The deputy commander of the Azov regiment, who was among the troops remaining in Mariupol, said the Russian military dropped heavy bombs on the steel plant and hit an “improvised” hospital.

Serhiy Taruta, the former governor of the Donetsk region and a Mariupol native, also reported the bombing of the hospital, where he said 300 people, including wounded troops and civilians with children, were sheltered.

The eastern cities of Kharkiv and Kramatorsk also came under deadly attack. Russia said it struck areas around Zaporizhzhia and Dnipro west of the Donbas with missiles.

Russian Defense Ministry spokesman Maj. Gen. Igor Konashenkov said the targets included troop concentrations and missile-warhead storage depots, in or near several cities or villages. Those claims could not be independently verified.

Both sides have described the assault that began Monday as a new phase of the war.

Ukrainian President Volodymyr Zelenskyy said the Russian military was throwing everything it has into the battle, with most of its combat-ready forces now concentrated in Ukraine and just across the border in Russia.

“They have driven almost everyone and everything that is capable of fighting us against Ukraine,” he said in his nightly video address to the nation.

Despite claims that they are hitting only military sites, the Russians continue to target residential areas and kill civilians, he said.

“The Russian army in this war is writing itself into world history forever as the most barbaric and inhuman army in the world,” Zelenskyy said.

He also said the Kremlin has not responded to a proposal to exchange Viktor Medvedchuk, the jailed leader of a pro-Russia party, for the Mariupol defenders.

Weeks ago, after the abortive Russian push to take Kyiv, the Kremlin declared that its main goal was the capture of the mostly Russian-speaking Donbas, where Moscow-backed separatists have been fighting Ukrainian forces for eight years.

A Russian victory in the Donbas would deprive Ukraine of the industrial assets concentrated there, including mines, metals plants and heavy-equipment factories.

A senior U.S. defense official, speaking on condition of anonymity to discuss the Pentagon’s assessments of the war, said the Russians had added two more combat units, known as battalion tactical groups, in Ukraine over the preceding 24 hours. That brought the total units in the country to 78, all of them in the south and the east, up from 65 last week, the official said.

That would translate to 55,000 to 62,000 troops, based on what the Pentagon said at the start of the war was the typical unit strength of 700 to 800 soldiers. But accurately determining Russia’s fighting capacity at this stage is difficult.

A European official, likewise speaking on condition of anonymity to discuss military assessments, said Russia also has 10,000 to 20,000 foreign fighters in the Donbas. They are a mix of mercenaries from Russia’s private Wagner Group and Russian proxy fighters from Syria and Libya, according to the official.

While Ukraine portrayed the attacks on Monday as the start of the long-feared offensive in the east, some observers noted that an escalation has been underway there for some time and questioned whether this was truly the start of a new offensive.

The U.S. official said the offensive in the Donbas has begun in a limited way, mainly in an area southwest of the city of Donetsk and south of Izyum.

Justin Crump, a former British tank commander now with the strategic advisory company Sibylline, said the Ukrainian comments could, in part, be an attempt to persuade allies to send more 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,’” Crump said. “That partly puts pressure on NATO and EU suppliers to say, ‘Guys, we’re starting to fight now. We need this now.’”

President Joe Biden is expected to announce a new weapons package in the coming days that will include additional artillery and ammunition, according to a U.S. official, who was not authorized to comment publicly and spoke on the condition of anonymity.

Canada and the Netherlands also planned to send more heavy weapons, their prime ministers said.

Associated Press journalists in Kharkiv said at least four people were killed and three wounded in a Russian attack on a residential area of the city.

An explosion also rocked Kramatorsk, killing at least one person and wounding three, according to AP journalists at the scene.

In the southern city of Bashtanka, an unspecified number of people were wounded when Russian forces shelled the hospital, destroying the reception area and the dialysis unit, the head of the regional council, Hanna Zamazeeva, said on Facebook.

Eyewitness accounts and reports from officials have given a broad picture of the extent of the Russian advance. But independent reporting in the parts of the Donbas held by Russian forces and separatists is severely limited, making it difficult to know what is happening in many places on the ground.

Military experts said the Russians’ goal is to encircle Ukrainian troops from the north, south and east.