Two northern neighborhoods were heavily shelled Sunday, leading to the casualties and damaging both residential and administrative buildings, the council said.
Fighting centered on Donetsk's government-held airport has left many northern neighborhoods in the crossfire. Over the weekend, Ukraine said its troops repelled an attack of 200 rebel fighters, but suffered no military casualties.
Observers from the Organization for Security and Co-operation in Europe say they were 200 meters (650 feet) away from four shells bursting Sunday in Donetsk. The team saw one woman lying on the ground, and said a rebel fighter on the scene told them four people had been killed that day.
The government has not confirmed the number of casualties.
The fighting began a month after Russia annexed the Black Sea peninsula of Crimea in March. It has claimed at least 3,000 civilian lives and forced hundreds of thousands to flee, according to the UN.
Meanwhile, German Chancellor Angela Merkel's spokesman said when asked about the Ukrainian defense minister's remarks that some NATO countries were sending arms that the German government has no knowledge of any country delivering weapons to the Ukraine government.
"The question of whether weapons are being delivered should be directed to the countries that supposedly or allegedly are doing it. We are not one of those countries and I know of no such thing," said Merkel's spokesman Steffen Seibert.
Ukraine's Defense Minister Valery Heletey said on Sunday that NATO countries were sending weapons to his country to help it fight pro-Russian separatists, following what he said were bilateral meetings with NATO defense ministers during a NATO summit in Wales on Sept. 4-5.
NATO officials have said the Western alliance will not send "lethal assistance" to non-member Ukraine but member states may do so.