Three people were killed and many more wounded when a shell hit a hospital in the rebel-held city of Donetsk in eastern Ukraine.
Bodies could be seen under blankets outside the building after the attack.
Violence has surged in recent weeks, and the pro-Russian rebels are trying to encircle the key town of Debaltseve, north-east of Donetsk.
EU foreign policy chief Federica Mogherini appealed for a truce to allow civilians to leave the area.
Her words echoed an appeal by international observer group the OSCE on Tuesday for a three-day ceasefire around the town.
According to Amnesty International, 7,000 people remain in Debaltseve, a major road and rail hub, out of an original population of 25,000 a few days ago.
The sound of shelling could still be heard two hours later, she said.
Residential areas of the two main rebel-held cities of Donetsk and Luhansk have regularly been hit by mortar rounds and rocket fire and the separatists have blamed the government for the attacks.
At the scene: Olga Ivshina, BBC News
Dozens of people were queuing to see their doctors at the Outpatient's clinic when the shell landed beside the building.
It left a crater and shattered glass causing deaths and injuries.
What was a multi-storey building, now looks like a shell with every window blown out.
It's not clear when the hospital will be back in operation, but what is clear, is that the indiscriminate shelling of densely populated areas continues unabated.
Whoever calls for a ceasefire on humanitarian grounds may be disappointed. Heavy explosions could still be heard in the area while the dead and wounded were being evacuated.
The separatists have already captured Donetsk airport from government forces in the past few weeks.
The hospital in the south-western Kirovskiy area of Donetsk was being used as an outpatient clinic at the time of the attack and many of the injured were patients and staff, BBC correspondent Olga Ivshina reports from the scene.
The OSCE said on Tuesday that it had found evidence of cluster munitions used in a 27 January attack on Luhansk.
Ukrainian officials responded by insisting that soldiers did not fire on civilian areas and did not use cluster munitions.
Ashton Carter, President Barack Obama's nominee as new US defence secretary, said on Wednesday that he was "inclined" to provide weapons to Ukraine to help Kiev in its fight with pro-Russian separatists.
Speaking before the Senate Armed Services Committee, Mr Carter said "we need to support the Ukrainians in defending themselves".
But he did not specify the nature of the weapons he had in mind.
The Obama administration has so far only provided non-lethal assistance to Ukraine which includes night-vision goggles, body armour and other items.
Senior officials and officers have been urging the president to increase US military assistance to include light-armour missiles designed to take out tanks and armoured vehicles.
More than 5,000 people have been killed in a conflict which began in the east last April, when separatists seized government buildings after Russia announced it had annexed the Ukrainian peninsula of Crimea.
Russia's move on Crimea followed the toppling of President Viktor Yanukovych in Kiev.
Ukraine and the West accuse Russia of fomenting the violence in the east with weapons and soldiers, although that is denied by the government in Moscow.
Ukraine's President Poroshenko has said he is confident that the US will start sending lethal weapons to help government forces, although no decision has been made in Washington.
Secretary of State John Kerry is due to visit Kiev on Thursday amid reports that President Barack Obama is reviewing an earlier decision not to send weapons.
Ukraine's war: The human cost
- 5,358 people killed and 12,235 wounded in eastern Ukraine
- Fatalities include 298 people on board flight MH17 shot down on 17 July
- 224 civilians killed in three-week period leading up to 1 February
- 5.2 million people estimated to be living in conflict areas
- 921,640 internally displaced people within Ukraine, including 136,216 children
- 600 000 fled to neighbouring countries of whom more than 400,000 have gone to Russia
Source: Figures from UN High Commissioner for Human Rights 3 February, and UN report, 21 January