The fighting between Russia-backed separatists and government troops in eastern Ukraine resumed in January after a month of relative calm, killing more than 200 people in the past three weeks, according to the United Nations.
The city hall in Donetsk said the number of casualties from Wednesday's shelling in the west part of Donetsk early afternoon was not immediately established but the rebel-run Donetsk News Agency reported five killed inside and near the hospital in Tekstilshchik district.
An Associated Press reporter who arrived on the scene shortly after the attack found one body covered by a sheet on the ground several meters from the building, near a crater from a projectile. The hospital was damaged by shrapnel and windows were shattered.
In the wake of the shelling, European Union foreign policy chief Federica Mogherini called for the withdrawal of heavy weaponry from Ukrainian cities and a truce for at least three days to ensure the safe evacuation of civilians from the conflict zone.
"The spiral of ever increasing violence in Eastern Ukraine needs to stop," she said in a statement. "The shelling of civilians, wherever it happens, is a grave violation of international humanitarian law. Artillery should immediately be withdrawn from residential areas."
As the conflict intensifies Ukrainian President Petro Poroshenko says he is confident that the United States will agree to send weapons to his country to help it fight pro-Russian rebels, a step the Americans reportedly are considering.
On a visit to a government-controlled city in eastern Ukraine on Tuesday, Poroshenko said that his government badly needs the lethal aid to help repel the separatist attacks in the conflict that that has left 5,300 people dead.
U.S. President Barack Obama has opposed sending lethal assistance to Ukraine's government, but a senior administration official told The Associated Press earlier this week the surge in fighting has spurred the White House to review the policy.
Poroshenko will have an opportunity on Thursday to make his case to U.S. Secretary of State John Kerry, who is scheduled to visit Kiev.
"I don't have a slightest doubt that the decision to supply Ukraine with weapons will be made by the United States as well as by other partners of ours," he said on a visit to Kharkiv, "because we need to have the capabilities to defend ourselves."
German Chancellor Angela Merkel on Tuesday said that she was opposed to the idea.
In Kiev, military spokesman Vladislav Seleznev said two Ukrainian troops have been killed and 18 injured in the past 24 hours. The most intense fighting is now focused about the railway hub of Debaltseve where, according to Seleznev, the rebels mounted an offensive against Ukrainian troops.
In Donetsk, separatist official Eduard Basurin told reporters that four civilians have been killed in the past days before Wednesday's shelling.
Balint Szlanko in Donetsk, Ukraine, and Nataliya Vasilyeva in Moscow contributed to this report.
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