AP reporters saw the bodies of two people killed while waiting for a bus in the separatist-held city of Donetsk.
Separatist authorities said another person died from an attack elsewhere in the city. Regional authorities loyal to the government said six people in total, including the three counted in Donetsk, had died throughout the day.
Fighting spiked over the weekend in the bitter battle for control over Donetsk's now-shattered airport. The level of artillery exchanges has abated since that peak.
The resurgence in fighting during the last few days led "to a threatening situation," Steinmeier said in Berlin.
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Negotiating stakes for the warring parties hinge on the terms of a cease-fire deal drawn up in September in the Belarusian capital, Minsk. Agreement was ostensibly reached over a line of contact between the opposing forces, although that has been insufficient to prevent continued fighting.
A new truce reached in December swiftly unravelled after the New Year and culminated with the confrontation that is still continuing at Donetsk airport and surrounding areas. Separatists insist they are entitled to control over the terminal, which now remains little more than a smoldering shell, while Ukraine says the Minsk deal makes no provisions for the airport.
Russia's Interfax news agency cited Russian ministry spokesman Maj Gen Igor Konashenkov as calling claims that troops had been sent into Ukraine as "absolute nonsense."
While Moscow has routinely denied supplying manpower and weapons to separatists in Ukraine, the sheer quantity of powerful arms in rebel hands has long strained those assertions. Numerous Russian citizens actively participate in combat in rebel formations, but Russia insists they are there on a voluntary basis.