DONETSK, Ukraine (CNN) -- The deadly battle for control of an airport in the Ukrainian city of Donetsk may have ended, but fears of further violence stalked the streets Wednesday as a military jet flew low overhead.
Dozens of pro-Russia separatists were killed after Ukrainian security forces launched an assault on Donetsk International Airport on Monday, following the militants' seizure of a terminal.
The bullets stopped flying Tuesday, but the roar of the military jet's engines fed into a narrative being sold by the separatists' spokespeople of a possible bombing campaign against the city.
There has been no indication by the Ukrainian authorities of any such plan.
But amid a climate of fear, distrust and misinformation, and in the aftermath of Monday's assault on the airport -- perhaps the deadliest incident in weeks of unrest -- concern in Donetsk is heightened.
There were unconfirmed reports Wednesday of some shots being fired not far from a central administration building occupied by the separatists for some weeks.
A representative for the separatists said they were trying to shoot down a drone.
The Ukrainian military's move against the militants at Donetsk airport has been interpreted by some as an indication that newly elected President Petro Poroshenko will take a tougher stance.
The presence of military aircraft may be intended as a reminder of the security forces' capacity to act.
The separatists' attempt to take the airport came within hours of Poroshenko claiming victory in Sunday's vote.
Donetsk has been at the heart of the separatists' bid to declare independence for the wider Donetsk region from the rest of Ukraine, which was mirrored in the neighboring Luhansk region.
Ukrainian Foreign Ministry spokesman Yevhen Perebynis said Wednesday that four international monitors who went missing Monday evening in the Donetsk region are being held by a pro-Russian group.
"The negotiations for their release are in process," Perebynis said during a briefing in Kiev.
The Organization for Security and Co-operation in Europe raised the alarm Tuesday, saying the team of four -- of Swiss, Turkish, Estonian and Danish nationality -- was on a routine patrol east of Donetsk city when it was last heard from.
The last time an OSCE team went missing in Donetsk, its members turned up in the hands of militant separatists in the town of Slovyansk. They were freed just over a week later.
Signs of the fierce fighting around the airport were visible in Donetsk on Tuesday. Blood and human remains could be seen near two blown-out trucks that had carried separatists.
A pile of bodies lay in a city morgue, including the remains of a woman whose head had been apparently taken off by a round.
One resident, who didn't want to show his face on camera, told a CNN team on the ground that many people in the region would be fighting -- and he didn't know who could stop the conflict, except perhaps Russia.
Asked whether he thought the eastern region could ever be part of a united Ukraine again, he replied, "I think Ukraine will be destroyed."
Other onlookers said the dead were "nashi," Russian for "our guys," in an indication of the public support the separatists command in their battle against the federal authorities. Eastern Ukraine was the support base for ousted pro-Moscow President Viktor Yanukovych, and many Russian speakers there feel closer to Moscow than to Kiev.
The Donetsk mayor's office said that 40 people had died in the airport fighting, including two civilians, but did not specify how many of the dead were separatists.
The separatists said that 35 of their own had been killed and about 60 more injured.
The separatist movement in Donetsk believed it was offered a three-hour truce Tuesday afternoon to leave the city of Donetsk, according to a spokeswoman for the self-declared Donetsk People's Republic who asked not to be identified to avoid possible arrest.
The Donetsk People's Republic 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 government's anti-terror operation told CNN there is a longstanding offer of amnesty to separatists who turn themselves in and give up their weapons, unless they are guilty of murder.
NATO: Signs of Russian troops packing up
Kiev and the West have accused Russia of backing and supplying the separatists, a claim Moscow denies.
They have also voiced concern over a buildup of what NATO estimated was 40,000 Russian troops near Russia's border with Ukraine.
In a sign that Russia may have heeded calls for it to withdraw those forces, NATO said Wednesday that there was "ongoing evidence of equipment and supplies being packed or prepared for movement" in the area.
"A small number of units have now withdrawn from the border. The activity we are observing continues to suggest a slow withdrawal of forces," a NATO military officer said.
However, he said, many of the Russian troops remain in the border area and are capable of operations at short notice. "Thousands of troops have withdrawn, but tens of thousands remain," he said.
The Kremlin announced about 10 days ago that Russian President Vladimir Putin had ordered tens of thousands of Russian troops to return to their bases but said the pullback could take some time.
NATO is monitoring the situation and would welcome a complete, verifiable Russian withdrawal, the NATO military officer said.
But, he added, "Any withdrawal does not erase or reverse what has happened in recent months. Russia has violated the trust of the international community by illegally invading Ukraine. The security dynamic in Europe has been fundamentally changed."
Ukraine is not part of NATO, but other former Soviet states such as Poland do belong to the alliance. Russia is opposed to any move by Ukraine to forge closer ties with NATO.
-- CNN's Nick Paton Walsh reported from Donetsk and Laura Smith-Spark wrote from London. Journalist Victoria Butenko contributed from Kiev and CNN's Andrew Carey from Donetsk.
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