Shelling killed six people and wounded 15 others in the rebel stronghold of Donetsk, the city council said Monday -- the worst reported violence since a cease-fire between Russian-backed rebels and Ukrainian troops took effect on Sept. 5.

Fighting around the eastern city's government-held airport has left its northern neighborhoods in the crossfire. Two northern neighborhoods were shelled heavily Sunday, leading to the casualties and damaging both homes and offices, the city council said.

Loud blasts could be heard from the direction of the airport all day Monday, and gunfire intermittently rang out downtown in the afternoon.

The Ukrainian government blamed the militants for the civilian casualties.

"Neither today, nor yesterday, nor in the previous days did Ukrainian forces shell any residential areas," said Lysenko.

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 Monday, NATO Secretary-General Anders Fogh Rasmussen told The Associated Press that  "around 1,000" Russian soldiers remain in Ukraine.

"While the Russians may have withdrawn some of their troops in Ukraine, there is a still Russian military presence within Ukraine," Rasmussen said in Brussels, adding that several thousand Russian soldiers were also along the border with Ukraine.

Still, the cease-fire deal has brought some benefits. Another 73 Ukrainian soldiers were freed Sunday in exchange for 73 rebels, both sides reported Monday -- the largest prisoner exchange so far.

And in neighborhoods away from the Donetsk airport, many more people and cars were out in the streets than have been for weeks.

The fighting in eastern Ukraine began in mid-April, a month after Russia annexed the Black Sea peninsula of Crimea. It has claimed at least 3,000 civilian lives, according to the U.N.