Ukraine’s interior ministry says the military is now in full control of the airport in the eastern city of Donetsk after a day of bloody clashes.
At least 30 pro-Russia separatists have been killed, the insurgents say. Kiev said the army suffered no casualties.
Armed separatists had tried to take over the airport early on Monday.
Ukraine’s new President Petro Poroshenko then vowed to tackle “terrorists” in the east “within hours, not months”.
Russian Foreign Minister Sergei Lavrov on Tuesday again called on Mr Poroshenko to stop military operations in eastern Ukraine immediately and implement a roadmap for peace negotiated in Geneva on 17 April.
Speaking at a news conference in Moscow, he said a “real war” was under way in the eastern Donetsk and Luhansk regions.
The regions declared independence after Russia annexed the Crimean peninsula in the wake of the removal of Ukraine’s pro-Moscow President Viktor Yanukovych.
President’s vow
Interior Minister Arsen Avakov said in a statement: “The airport is under our full control. The enemy suffered heavy losses. We have none.”
Pro-Russia militants tried to take over the airport early on Monday morningHe said operations were still continuing, and a BBC team heard sporadic gunfire on Tuesday.
A representative of the self-proclaimed Donetsk People’s Republic told the BBC that reports of at least 30 dead in Monday’s fighting were accurate.
Other reports of the death toll vary.
Donetsk mayor Alexander Lukyanchenko said 40 people had been killed in the past day, while another separatist spokesman said 50 fighters had died.
Monday’s clashes started after separatist militants stormed the Sergei Prokofiev Donetsk airport in the early hours.
The separatists may have been trying to prevent a visit by the new president
The Donetsk ice hockey stadium was set on fire on Tuesday, reportedly after an armed group broke inThe Ukrainian military responded quickly with air strikes and an assault by heavily armed troops.
The attempt to seize the airport may have been intended to prevent Mr Poroshenko from travelling there after he said his first trip would be to visit the restive east.
Mr Poroshenko, a 48-year-old billionaire and former foreign minister, was on Monday formally declared the winner of Sunday’s presidential election with 54% of the vote.
He vowed east Ukraine would not be “turned into Somalia”, adding: “The anti-terrorist operation cannot and should not last two or three months. It should and will last hours.”
Petro Poroshenko: “We will fight for the trust of the people” of the east
However, Mr Poroshenko has also said he wants to talk to Russia to end the crisis.
Moscow says it will accept the election results and engage in dialogue with Mr Poroshenko.
But Mr Lavrov said: “The question of a visit to Russia by Poroshenko is not being considered and is not being discussed through diplomatic or any other channels.”
The insurgency developed after Mr Yanukovych fled Kiev amid bloody street protests and calls for closer ties with the EU.
At least two civilians were killed in Donetsk city and the separatist stronghold of Sloviansk on Monday.
The body of a woman, reportedly killed by a stray bullet, lay near the railway in station Donetsk
In Sloviansk, the bloodied body of another woman lay near an apartment block. At least one man was also wounded.
