According to Donetsk Mayor Alexander Lukyanchenko, dozens of other people were injured in the government's operation to retake the international airport of the city.
The battle began Monday when Ukrainian troops launched airstrikes against armed activists, who took control of the airport earlier in the day and responded with automatic weapons and grenades.
By early Tuesday, government troops had forced the militants to withdraw from the airport and brought it under their control.
The clashes happened just one day after a presidential election was held in the eastern European country.
Preliminary results showed independent politician Petro Poroshenko was a likely winner, taking a comfortable lead with 54.45 percent of over 95 percent of the ballots accounted. Former prime minister Yulia Tymoshenko conceded defeat with only 12.8 percent of the vote.
On Monday, Poroshenko said he wanted to negotiate with protestors to end the crisis, but emphasised he would not talk with terrorists.