The vehicles sped through red lights and shops closed early because of shelling, which followed an intense exchange of gunfire near a shopping mall in the city.
Meanwhile, 17 bodies have so far been recovered from the wreckage of a Ukrainian refugee convoy that was hit by shelling on Monday, a military spokesman said.
Six others were being treated in hospital for injuries, of whom three were in a serious condition.
Ukrainian president Petro Poroshenko yesterday confirmed he would meet Russian president Vladimir Putin at a meeting in Minsk, Belarus, next week.
Mr Poroshenko said "stabilising the situation" in eastern Ukraine where fighting has claimed more than 2,000 lives would be a key topic of discussion.
The two men have not met since early June.