Forty people were killed in a violent clash between pro-Russia rebels and government forces at the Donetsk airport in east Ukraine on Monday and Tuesday.

At least 40 are dead and 31 have been injured, including four civilians, in what has been the deadliest outbreak of violence so far in weeks of fighting.

The conflict began when pro-Russia separatists took over the Donetsk International Airport hours after billionaire businessman Petro Poroshenko was elected as the new Ukrainian president.

Ukrainian forces tried to stop the militants Monday, with a bloody battle waging into the night.

The airport closed Tuesday due to the gunfire.

A spokesperson for the self-declared separatist group, the Donetsk People's Republic, told CNN that 35 separatists were killing in the fighting and 60 were injured.

The Ukrainian military began to regain control of the airport Tuesday, with Ukrainian Minister Arsen Avakov saying that the "Airport in Donetsk is fully under our control."

Two trucks were blown up by heavy weapons, which may have caused some of the casualties Monday.

The rebels in Donetsk said they were offered a three-hour truce Tuesday to leave the city. A spokeswoman, who asked not to be identified, said the truce was offered between 1 and 4 p.m. local time.

She said the Ukrainian forces are threatening to bomb separatist areas of the city if they do not leave.

Yet, the Ukrainian government denied that they offered the separatists a truce. The Ukraine Government's Anti-Terror Operation said they're offering amnesty to rebels who turn themselves in and give up their weapons, unless they committed murder.

In another part of Donetsk, the Organization for Security and Cooperation in Europe said it has not had contact with one of its Donetsk-based teams since 6 p.m. Monday. A team of four foreign individuals were on a patrol of east Donetsk when they were last seen or heard from.

A NATO official also reported that it appears like Russia is moving, or preparing to move some of its troops away from the Ukraine border. The official said that there are signs of Russian equipment being packed or prepared to move.

While it appears like the new president is cracking down on militants in the east, his latest push against the rebels is not welcomed by Russia.

Russian President Vladimir Putin said Tuesday that Ukraine should stop all operations against separatists in the east.

Ukraine and the West have accused Russia of backing the rebels, but Russia has denied having any direct influence over the militants.

President Poroshenko said at a news conference Monday that Russia needs to participate in brokering peace in regions in east Ukraine that declared autonomy from the country a few weeks ago.

Poroshenko added that his administration will focus on becoming more integrated with the European Union.