Shelling has killed six people and wounded 15 others in the rebel stronghold of Donetsk, the city council said, the worst reported violence since a ceasefire between Russian-backed rebels and Ukrainian troops began on September 5.
Fighting around the eastern city's government-held airport has left its northern areas in the crossfire.
The city council on Monday said that two northern areas were shelled heavily, leading to the casualties and damaging both homes and offices.
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Loud blasts could be heard from the direction of the airport all day Monday, and gunfire intermittently rang out in the city centre in the afternoon.
The Ukrainian government blamed the fighters for the civilian casualties.
"Neither today, nor yesterday, nor in the previous days did Ukrainian forces shell any residential areas," said Col. Andriy Lysenko, spokesman for the Ukrainian defence council.
Both the rebel and government sides have said they are rearming in case the fighting starts anew.
Ukraine and the West have repeatedly contended that Russia is fueling the separatist uprising with manpower, weapons and expertise, something that Moscow denies.
In an interview on Monday, the NATO secretary general Anders Fogh Rasmussen told the AP news agency that about 1,000 Russian soldiers remain in Ukraine.
"While the Russians may have withdrawn some of their troops, there is a still Russian military presence," he said in Brussels, adding that several thousand Russian soldiers were also along the border with Ukraine.
The Russian president, Vladimir Putin, and German chancellor Angela Merkel in a phone conversation on Monday both stressed the importance of observing the cease-fire, the Kremlin said in a statement.
The Kremlin did not mention the frequent violations.
Merkel said she had told Putin that Russia must withdraw its troops from Ukraine for the peace plan to work.
She said the complete withdrawal must accompany a securing of the Russian-Ukrainian border to prevent fighters and arms flowing to pro-Russian separatists in eastern Ukraine.