Story highlights OSCE loses touch with team of four international monitors in Donetsk

Donetsk morgue contains bodies torn apart by bullets, shrapnel, explosions

40 people killed, two of them civilians, in airport gun battle, Donetsk mayor's website says

35 militants killed and about 60 injured in Monday's fighting, separatists say

A battle between pro-Russia separatists and government forces at Donetsk airport in eastern Ukraine has claimed 40 lives, authorities said Tuesday, in what is the deadliest outbreak of violence yet in the flashpoint city.

An additional 31 people have been injured, including four civilians, according to the website of the Donetsk mayor, Alexander Lukyanchenko. Two of the fatalities are civilians.

The conflict at Donetsk International Airport broke out only hours after newly elected Ukrainian President Petro Poroshenko said he'd potentially like to negotiate a way out of the crisis.

After Ukrainian forces moved in against the militants Monday, the deadly assault continued overnight.

The airport remained closed Tuesday despite an easing in the gunfire, as conflicting accounts emerged of how many had lost their lives.

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Photos: Photos: Ukraine after the election Photos: Photos: Ukraine after the election Ukraine after the election – Ukrainian soldiers sit on an armored vehicle as they take up a position in a sunflower field near Donetsk, Ukraine, on Thursday, July 10. Here's a look at the upheaval that has persisted in eastern Ukraine since the election of President Petro Poroshenko. Hide Caption 1 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – A man rides a bike past the tail of a bombshell outside Slovyansk, Ukraine, on July 10. Hide Caption 2 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – Eugenia Gubareva cries on July 10 after finding clothes belonging to her parents, who were killed during a bomb shelling in Mikolaivka, Ukraine. Hide Caption 3 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – A man cleans up debris in his apartment after a shelling in Slovyansk on July 10. Hide Caption 4 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – People walk under a destroyed railroad bridge near the village of Novobakhmutivka on Monday, July 7. Hide Caption 5 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – A woman cries as her house burns after a bombing in Slovyansk on Monday, June 30. Hide Caption 6 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – People say goodbye to volunteer soldiers in Kiev, Ukraine, before they leave for the eastern part of the country to join the ranks of a special battalion on Monday, June 23. Hide Caption 7 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – People take refuge in a bomb shelter during clashes between Ukrainian troops and pro-Russia fighters in Slovyansk on Sunday, June 22. Hide Caption 8 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – Riot police surround the Kiev Pechersk Lavra, an Orthodox Christian monastery in Kiev where radical masked activists gather to protest against separatists on June 22. Hide Caption 9 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – Ukrainian President Petro Poroshenko awards wounded soldiers with state awards in a military hospital in Kiev on Saturday, June 21. Hide Caption 10 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – Debris lies scattered at an airport in Luhansk, Ukraine, on Saturday, June 14, after the crash of a Ukrainian Ilyushin-76 military transport plane. A military spokesman said the aircraft was shot down by pro-Russian separatists, killing all 49 aboard. Hide Caption 11 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – A pro-Russian fighter collects ammunition from the debris of the downed military aircraft on June 14. Hide Caption 12 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – Pro-Russian fighters walk past the wreckage of the downed aircraft. Hide Caption 13 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – A military vehicle was destroyed during a clash between Ukrainian troops and pro-Russian separatists Friday, June 13, in Mariupol, Ukraine. Hide Caption 14 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – Locals in Mariupol gather around a burning military vehicle at the site of a battle between Ukrainian troops and pro-Russian fighters on June 13. Hide Caption 15 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – A pro-Russian fighter in Slovyansk checks a woman's documents as she leaves the city on Thursday, June 12. Hide Caption 16 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – A pro-Russian fighter stands guard at a checkpoint in Slovyansk on June 12. Hide Caption 17 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – A girl looks out of a bus window as she leaves Slovyansk on Monday, June 9. Hide Caption 18 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – Poroshenko holds the ceremonial mace during his inauguration ceremony Saturday, June 7, in Kiev. Poroshenko was elected three months after the ouster of former President Viktor Yanukovych. Hide Caption 19 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – A Ukrainian tank opens fire during a battle with pro-Russian separatist fighters in Slovyansk on Friday, June 6. Hide Caption 20 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – A Ukrainian soldier prepares explosives during a battle with pro-Russian separatists in Slovyansk on June 6. Hide Caption 21 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – A Ukrainian soldier observes the road at a checkpoint outside of Amvrosiivka, Ukraine, on Thursday, June 5. Hide Caption 22 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – Ukrainian soldiers take position during a battle with pro-Russian separatists outside Slovyansk on June 5. Hide Caption 23 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – Pro-Russian militants stand guard at a barricade and checkpoint in Donetsk on Sunday, June 1. Hide Caption 24 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – A Ukrainian soldier shoots a grenade launcher during a battle with pro-Russian separatists in Slovyansk on Saturday, May 31. Hide Caption 25 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – A protester from Kiev's Independence Square gestures May 31 as fellow protesters burn tires to protect their barricades from being dismantled by communal services. Hide Caption 26 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – A Ukrainian armored personnel carrier takes position during a battle with pro-Russian separatist fighters May 31 in Slovyansk. Hide Caption 27 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – Ukrainian soldiers rest at a checkpoint outside Slovyansk on Thursday, May 29. Hide Caption 28 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – Smoke rises from a shot-down Ukrainian Army helicopter outside Slovyansk on May 29. Hide Caption 29 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – A man stands in front of a truck that was bombed by Ukrainian soldiers during clashes with armed rebels Tuesday, May 27, in Donetsk. Hide Caption 30 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – Medical staff prepare to clean the body of a pro-Russian militant at the Kalinina morgue in Donetsk on May 27. Hide Caption 31 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – The body of a pro-Russian militant lies on a stretcher at a morgue in Donetsk on May 27. He was killed in clashes around Donetsk's airport, which was seized by pro-Russian separatists a day earlier. Ukrainian forces moved in and reclaimed the facility. Hide Caption 32 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – Firefighters work on extinguishing a fire at a local sports hall in Donetsk on May 27. Hide Caption 33 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – People pile up sandbags to set up a shooting position on the road leading from the Donetsk airport on May 27. Hide Caption 34 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – A man dressed in a prisoner costume takes part in a protest against government corruption May 27 in Kiev. Hide Caption 35 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – Pro-Russian militants take position on the roof of Donetsk International Airport on Monday, May 26. Hide Caption 36 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – A pro-Russian militant takes position on the roof of the Donetsk airport on May 26. Hide Caption 37 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – A man runs for cover during fighting around the airport on May 26. Hide Caption 38 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – Smoke rises from the airport on May 26 after an airstrike by the Ukrainian military. Hide Caption 39 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – Pro-Russian gunmen take positions near the airport on May 26. Hide Caption 40 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – Men stand next to pro-Russian militants as a woman runs away during clashes near the airport on May 26. Hide Caption 41 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – A pro-Russian militant guards a checkpoint on May 26, blocking a highway that links the Ukrainian city of Kharkiv with Rostov-on-Don, Russia. Hide Caption 42 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – A pro-Russian militant teaches recruits how to use a machine gun in Senyonovka, Ukraine, on May 26. Hide Caption 43 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – A woman walks May 26 near barricades built by protesters in Kiev's Independence Square. Vitali Klitschko, Kiev's future mayor and a former boxing champion, promised to dismantle the iconic protest encampment that helped oust Yanukovych but now clogs traffic and draws public complaints. Hide Caption 44 of 50 Photos: Photos: Ukraine after the election Ukraine under new elected leadership – Ukraine's newly elected president, Petro Poroshenko, talks alongside Klitschko, right, during a news conference in Kiev on May 26. Poroshenko, a billionaire candy tycoon known as the "Chocolate King," is a seasoned politician known for his pro-European Union views. Hide Caption 45 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – Election commission officials count ballots at a polling station in Kiev on Sunday, May 25. Hide Caption 46 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – Artist Ivan Voronov, 91, and his wife, Svetlana Samoilechenko, 86, cast votes from their Kiev home on May 25. Hide Caption 47 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – An elderly woman casts her vote May 25 as a mobile Ukrainian election committee visited Orane, a village north of Kiev. Hide Caption 48 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – A woman holds the hand of a pro-Russian gunman in Donetsk's Lenin Square on May 25. A large separatist rally was held in Donetsk around lunchtime. The protesters chanted pro-Russian slogans as they were addressed by separatist leaders. Hide Caption 49 of 50 Photos: Photos: Ukraine after the election Ukraine after the election – A man prepares a ballot at a polling station in the eastern Ukrainian town of Dobropillya on May 25. See the crisis in Ukraine before the election Hide Caption 50 of 50

The Donetsk mayor's website didn't specify how many of the 40 killed in the airport standoff were separatists.

But a spokeswoman for the separatist self-declared "Donetsk People's Republic" (DNR) told CNN that 35 separatists had been killed and about 60 injured in Monday's fighting.

Although the separatists earlier claimed they controlled the airport, it became clear as Tuesday wore on that the Ukrainian military had taken charge.

The official website of Ukrainian Interior Minister Arsen Avakov said late Tuesday the "Airport in Donetsk is fully under our control."

The occasional exchange of gunfire and blasts could be heard from the airport but it was not clear if the shots were fired by military as they maintained a perimeter or whether separatist forces were still present within its territory.

Two blown-out trucks nearby appeared to have been hit by heavy weapons. Human remains were still visible, suggesting this may have been the cause of some of the casualties Monday.

The separatist movement in Donetsk believed it was offered a three-hour 'truce' Tuesday to leave the city of Donetsk, according to a spokeswoman for the DNR who asked not to be identified to avoid possible arrest. The truce was offered between 1 and 4 p.m. local time (6 a.m. and 9 a.m. ET), she said.

The DPR learned of this truce online, the spokeswoman told CNN, adding that Ukrainian armed forces were threatening to bomb separatist strongholds in the city if they failed to leave.

The Ukrainian government denied offering rebels any such truce. The Ukraine Government's Anti-Terror Operation (ATO) told CNN there is a longstanding offer of amnesty to any separatist who turns himself in and gives up his weapons, unless he (or she) is guilty of murder.

Morgue piled with bodies

A CNN team at a morgue in Donetsk saw a large pile of separatist militant bodies, many of which had been torn apart by shrapnel and explosions.

Doctors there said 31 bodies had been brought in with different types of injuries, from bullet wounds to those caused by heavy weapons and explosions. The remains included the body of a woman civilian.

Doctors also said some locals had arrived during the morning to identify and collect their relatives from among the dead.

The airport clashes marked the worst violence that this key population center in eastern Ukraine has seen since the start of the crisis. A statement posted on the mayor's website Monday advised residents to stay in their homes as sounds of gunfire and explosions cracked through the air.

Elsewhere in the Donetsk region, the Organization for Security and Cooperation in Europe said it has had no contact with one of its Donetsk-based teams since around 6 p.m. (11 a.m. ET) Monday .

Where unrest has occurred in E. Ukraine

The team of four -- of Swiss, Turkish, Estonian and Danish nationality -- was on a routine patrol east of Donetsk when it was last heard from. The OSCE says it is using contacts on the ground to try to determine where the monitors are.

The last time an OSCE team went missing in Donetsk, its members turned up in the hands of militant separatists in the flashpoint town of Slovyansk. They were freed just over a week later.

In another development, NATO has observed Russian troop movement near the Russia-Ukraine border recently, a NATO officer told CNN. Speaking on condition of anonymity, the officer said this included signs of Russian equipment and supplies being packed or prepared for movement, and that the activity could signal a slow or staged withdrawal of forces.

Turning point?

The Ukrainian security forces' muscular airport assault may signal a shift in approach as the new president takes charge in Kiev.

A senior Ukrainian official told CNN's Jim Sciutto in Kiev that it is "now or never" in the fight against militants in the East.

"We have been patient for far too long," he said, indicating that with the election over, the new government believes it has a mandate to put the insurgency to rest.

U.S. Ambassador to Ukraine Geoff Pyatt told CNN that the crisis is now entering its "most kinetic phase."

At the same time, Russian President Vladimir Putin on Tuesday urged an immediate halt to the operation against separatist militants in Ukraine's south and east, the Kremlin said.

Putin also spoke by phone with Italy's Prime Minister Matteo Renzi of the need for the leadership in Kiev to start a peaceful dialogue with representatives of Ukraine's regions, it said.

Kiev and the West have accused Moscow of backing Ukraine's separatists. But Russia has denied having direct influence over the pro-Russia militants and says the unrest is due to the actions of far-right ultranationalists.

At a news conference Monday in Kiev, Poroshenko, the newly elected president, said that Russia needed to participate in bringing peace to eastern Ukraine.

He also reiterated that European integration would be his priority.

In addition to the unrest roiling the east, Poroshenko, a candy tycoon known as the "Chocolate King," faces the challenge posed by Ukraine's ailing economy and a looming crisis over Russia's supply of natural gas to Ukraine.

Russia's energy giant Gazprom says Ukraine owes it $3.5 billion for gas already supplied and has threatened to turn off the taps if no payment is made. But Ukraine's interim government has said that the price must be renegotiated after Russia hiked it up this spring.

Prime Minister Arensiy Yatsenyuk said on his website Tuesday that Ukraine would take the issue to an international court if Russia's Gazprom and his own country's Naftogaz do not sign an agreement by May 29.

Anti-aircraft weapons

Government air and ground forces attacked the pro-Russia militants after they seized a terminal at the airport early Monday.

The troops moved in after the separatists ignored a government ultimatum to vacate the premises, said the country's anti-terror office spokesman, Vladislav Seleznev.

After a Ukrainian military plane "made a preliminary shot," paratroopers landed and began clearing the airport, Ukrinform reported. In the fighting, a separatist anti-aircraft gun was destroyed , the news agency said.

Although the gunfire had largely halted by Tuesday morning, the airport is not expected to reopen for the moment.

The preliminary evaluation is that the airport suffered minor damage in the fighting, Seleznev said.

Experts are working to establish whether all the navigation and other systems are working, he said. In any case, it is not judged safe for airplanes to fly because the separatists have weapons capable of shooting at aircraft and seem willing to use them.

Seleznev also warned in a Facebook post Tuesday that if the rebels do not surrender, "terrorist" targets in Donetsk will be hit by "special high-precision weapons."

Government officials had been optimistic that flights would resume by 9 a.m. (2 a.m. ET) Tuesday, but given the situation, it remains unclear when the airport will reopen.

Ukraine's acting Interior Minister Arsen Avakov posted on his Facebook page Tuesday that an airstrike had destroyed a training camp in Yasenakh, in the Luhansk region.

Separatist unrest over recent weeks has centered in the country's Donetsk and Luhansk regions.

Internal reconciliation

U.S. President Barack Obama congratulated Ukrainians for casting their ballots Sunday and criticized Russia-backed separatists, whom he accused of trying to block voting.

German Chancellor Angela Merkel, in a phone call with Poroshenko, hailed the vote as "a clear commitment of the Ukrainian people to unity and democracy as well as a peaceful solution to the current conflict," Merkel's spokesman said in a statement.

She said Germany would continue to support Ukraine on its democratic path, the spokesman said, adding that the two leaders agreed on the need to pursue internal reconciliation through national dialogue and constitutional reform.

At a news conference Monday, OSCE Parliamentary President Joao Soares said the presidential election was fair and represented the will of the Ukrainian people, despite major problems in Donetsk and Luhansk.