Ukrainian forces fought with separatists in the city of Donetsk for a second day on Tuesday after inflicting heavy losses on the rebels and the government vowed to press on with a military offensive "until not a single terrorist" was left, according to Reuters. Pro-Russian rebels said more than 50 of their fighters had been killed. The mayor of Donetsk, an industrial hub in eastern Ukraine, said the death toll in the clashes which erupted on Monday stood at 40, including two civilians. Ukraine used air strikes and a paratroop assault on Monday to clear rebels from Donetsk's international airport and had pushed the separatists out of the complex by the end of the day. But shooting continued through the night and on Tuesday the road to the airport bore signs of fighting overnight and heavy machinegun fire could be heard in the distance in mid-morning. "The airport is completely under control," Interior Minister Arsen Avakov told journalists in the capital Kiev. "The adversary suffered heavy losses. We have no losses," he added.