The latest deaths came as international pressure grew for an immediate halt to surging violence that has seen hundreds of civilians killed in recent weeks as pro-Russian rebels pushed into government-held territory.
Four people were killed when a hospital in east Ukraine was shelled ahead of a visit to Kiev by US Secretary of State John Kerry that will focus on the possibility of arming Ukrainian forces.
President Petro Poroshenko said the events of recent days should encourage NATO to "provide more support to Ukraine, including the provision of modern weapons to protect itself and defend itself against the aggressor".
"We need a strong army with new weapons, this will help us to defend the civilian population against attacks by terrorists," he toldGerman newspaper Die Welt.
Hours before Kerry was due to arrive in Kiev, US President Barack Obama's nominee for defense secretary said he was likely to support providing Ukraine with weapons.
Ashton Carter, expected to be confirmed soon as Pentagon chief, told a US Senate committee that "we need to support the Ukrainians in defending themselves".
However, Vice President Joe Biden seemed less hawkish, telling German newspaper Sueddeutsche Zeitung: "We have said since the beginning that there is no military solution to this crisis."
Wednesday's violence occurred at a hospital in a western suburb of the rebel stronghold of Donetsk, where an AFP journalist saw a body lying next to the crater from a mortar blast that caused extensive damage to the building.
Two more dead civilians were sprawled outside a nearby residential building, and a local resident said another elderly man was killed in his home.
Eight other civilians were killed in clashes around the region in a 24-hour period, rebel and government officials said, and the army said four soldiers died and 25 were wounded.
EU foreign affairs head Federica Mogherini called for an immediate ceasefire to allow civilians to escape the fighting.
"The spiral of ever-increasing violence in eastern Ukraine needs to stop," Mogherini said.
Observers from the Organization for Security and Co-operation in Europe have demanded a "local temporary truce" around the battleground town of Debaltseve for the next three days.
Amnesty International said Debaltseve's population had dropped from 25,000 to 7,000 in just a few days.
The strategic railway hub between Donetsk and another rebel centre, Lugansk, has been the focus of the fiercest fighting for a week as rebels battle to encircle Ukrainian forces.
Officials say thousands of civilians have fled the beleaguered town over recent days and those remaining behind were trapped in basements without water or electricity.
"The bombardment is incessant. We are trying to bring in medication and evacuate civilians under enemy fire," Illya Kiva, an official from Ukraine's interior ministry, told AFP from Debaltseve.
Ukraine's military said rebels had launched a fierce infantry attack on the town overnight Tuesday but been beaten back after a five-hour battle.
'We need modern warfare'
Kerry will arrive in Ukraine on Thursday with hopes growing among Kiev's pro-Western leaders that long-standing demands for the US to supply weapons could be met.
President Barack Obama's administration had previously ruled out sending arms to Ukraine's government but the failure of economic sanctions to force Russia to halt Moscow's alleged military support for the separatists has prompted a second look at the option.
Washington -- fearful of becoming embroiled in a proxy war with Russia -- has so far provided non-lethal assistance to Ukraine, including flak jackets, medical supplies, radios and night-vision goggles.
Ukraine though is believed to be seeking weapons, including so-called "fire-and-forget" advanced anti-tank missiles, to counter the heavy armour it says Moscow has poured over the border.
"What we need is exactly modern warfare, which we've been lacking all this time," Ukraine's Foreign Minister Pavlo Klimkin told Western journalists in Kiev.
While Kerry is not expected to pledge any arms during his trip, Ukraine will take heart from Carter's comments.
Klimkin said he hoped for "deliverables" from the visit and from another meeting between Poroshenko and Biden in Munich.
Poroshenko said on Tuesday he had "no doubt" that the US and other NATO allies would eventually agree to start arming Ukraine.
Fears are mounting of a sharp escalation in the violence in eastern Ukraine after truce talks collapsed and rebels announced an ambitious mobilisation to start next week aimed at bolstering their forces to 100,000 fighters.
Fighting since last April has claimed more than 5,358 lives, including some 220 in just the past three weeks, according to the United Nations.
Ukraine and its Western allies accuse Moscow of sending thousands of regular army troops and weapons to support the rebels.
Moscow has repeatedly denied the allegations but the rebels appear to be equipped with the advanced weaponry of a regular army.
By Simon Valmary with Max Delany in Kiev (AFP)