KYIV, Ukraine (AP) -- Russian forces pressured a stubborn pocket of resistance in Mariupol amid renewed hopes Wednesday for an evacuation of thousands of civilians from the shattered port city that is a key battleground in Moscow's new onslaught to take control of Ukraine's eastern industrial heartland.
In addition to pounding Mariupol, Russian forces have intensified their attacks along a boomerang-shaped front hundreds of miles long in what is known as the Donbas, home to coal mines, metal plants and factories vital to Ukraine's economy.
If successful, the offensive would give President Vladimir Putin a badly needed victory following the failed attempt by Moscow's forces to storm the capital, Kyiv, and stronger-than-expected resistance in the nearly two-month war.
Ukrainian troops said Tuesday the Russian military dropped heavy bombs to flatten what was left of a sprawling steel plant -- believed to be the last holdout of troops defending Mariupol -- and hit a makeshift hospital where hundreds were staying. The reports could not be independently confirmed.
Elsewhere, Russian Defense Ministry said Wednesday its forces kept up intense attacks on Ukrainian targets, hitting 1,053 with artillery and 73 with airstrikes. Ministry spokesman Igor Konashenkov also said there had been missile strikes on concentrations of Ukrainian troops and vehicles in the Kherson Region in southern Ukraine. Those claims could not be independently verified.
The General Staff of Ukraine's military said in a statement that taking control of the Azovstal steel mill and thus fully capturing Mariupol remains a top Russian priority. But it added that Moscow's forces were continuing to mount offensives across the east as its forces probe for weak points in the Ukrainian defensive lines.
A siege on Mariupol since the early days of the war has flattened much of the city on the Sea of Azov and inflicted some of the most dramatic suffering of the conflict, which has also pushed more than 5 million people to flee the country.
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 and head west to the Ukraine-controlled city of Zaporizhzhia on Wednesday afternoon.
Mariupol Mayor Vadym Boychenko urged locals to leave the city, though previous such agreements have fallen apart, with Russians preventing buses meant to pick up evacuees from entering the city or shelling escape routes.
"Do not be frightened and evacuate to Zaporizhzhia, where you can receive all the help you need -- food, medicine, essentials -- and the main thing is that you will be in safety," he wrote in a statement issued by the city council.
Boychenko asked people who had already left Mariupol to contact relatives still in the city and urge them to evacuate. He said 200,000 people had already left the city, which had a pre-war population of more than 400,000.
Boychenko said buses would be used for the evacuation and one pickup point will be near the Azovstal steel mill, where a Ukrainian police official has said civilians, including children, are sheltering among the city's last known defenders.
Many previous evacuation efforts relied on civilians using private cars after efforts to bring buses from Ukraine-held territory into the city failed. But with fuel supplies and the number of such vehicles dwindling in the city, that is becoming increasingly difficult.
There was no immediate confirmation on the evacuation from the Russian side, which issued a new ultimatum to the Ukrainian defenders to surrender Wednesday. The Ukrainians have ignored previous demands to leave the sprawling steel plant's warren of tunnels and bunkers.
The Russian Defense Ministry said those who surrender will be allowed to live and given medical treatment.
Capturing Mariupol holds strategic and symbolic value for both sides. The scale of suffering there has made it a focal point of the war for many outside Ukraine, and Russia's difficulty in definitively taking it is a prime example of the ways an under-gunned Ukrainian force has stymied Moscow's troops.
Mariupol's fall would also deprive Ukraine of a vital port, complete a land bridge between Russia and the Crimean Peninsula that Moscow seized from Ukraine in 2014 and 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 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.
Both sides have described stepped-up assaults along a broad front in the east 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.
Military experts said the Russians' goal is to encircle Ukrainian troops from the north, south and east. Moscow has poured thousands more troops into Ukraine's south and east in recent days, including foreign fighters, according to Western officials.
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.
Western nations, meanwhile, are boosting their donations of military supplies to Kyiv.
U.S. 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.