Donetsk, Ukraine (CNN) -- Ukraine's President-elect Petro Poroshenko has vowed to punish the "bandits" who shot down a military helicopter as the government's efforts to rein in pro-Russia separatists continue.
"The deaths of the military troops in Slovyansk are pain our whole nation is feeling," Poroshenko posted on his Facebook page late Thursday.
"While mourning with rest of the Ukraine, I give my condolences to the families and loved ones of the fallen heroes. Crimes of the bandits will not be left unpunished."
Militants in the rebel stronghold of Slovyansk, in the Donetsk region, claimed responsibility for downing the helicopter, a spokesman for the separatists said. A dozen servicemen died, authorities said, including a general.
The separatist unrest that has gripped Ukraine in recent weeks has been centered in the eastern regions of Donetsk and Luhansk.
Acting Ukrainian Defense Minister Mikhail Koval said Friday that the military would continue its "anti-terrorism" operation until the east has been fully stabilized, Russia's state-run RIA Novosti news agency reported.
"We will work until this region starts living and functioning normally, and the people there feel safe," Koval is quoted as saying.
International monitors sent by the Organization for Security and Cooperation in Europe, at the invitation of Ukraine, have been surveying the situation on the ground -- but they appear increasingly at risk of being targeted by armed groups.
Four are said to be in the hands of pro-Russian separatists in Slovyansk, having gone missing Monday.
And Friday, the OSCE said it had also lost contact with some members of its Luhansk-based team as of the previous evening after armed men stopped them.
The team, which was in Severodonetsk, about 60 miles north of the city of Luhansk, consists of four international monitors and a Ukrainian translator, traveling in two vehicles, the OSCE statement said.
Another 11 monitors were detained for several hours Wednesday after armed men stopped them in Marinka, west of the city of Donetsk, but were later released, according to the OSCE.
Several weeks ago, another OSCE team was taken captive by militant separatists in Slovyansk. Its members were freed a little more than a week later.
Many are now looking at Poroshenko, whose inauguration is expected next week, to restore peace and stability to the divided nation.
Amid simmering tensions, heavily armed militants clashed with a National Guard unit Thursday in the town of Oleksandrivsk in the Luhansk region, the National Guard said on its website.
A grenade hit the unit's weapons depot, which exploded, destroying weapons and ammunition, the guard said. No casualties were reported.
On Monday, a Ukrainian military operation against pro-Russia militants who had seized a part of Donetsk International Airport resulted in as many as 70 deaths, according to the separatists, although local officials' estimates were lower.
At least 33 Russian citizens are among the militants killed, a spokesman for the self-declared Donetsk People's Republic told CNN. Their bodies are to be returned to Russia.
Kiev and the West have accused Russia of coordinating and supplying the separatists, an allegation Moscow has denied.
Russian troops 'pulling back'
On Thursday, a U.S. official with direct knowledge of the latest intelligence said 30,000 Russian troops that had been amassed along the Russia-Ukraine border have been moving back to their home bases over the past several days. About 10,000 troops -- mainly infantry -- remain along Russia's border with eastern Ukraine, the official said, and there are signs those troops will be pulling back as well.
NATO this week also reported that some Russian troops near Ukraine's eastern border may be preparing to pull back.
The United States has been using satellites to track Russian troop movements for weeks, and both the United States and NATO have released imagery to bolster their case that Russia had amassed tens of thousands of troops along the border.
U.S. officials have said it appears the Russians have decided to try to work with the new Ukrainian government, but officials also point out that it wouldn't take much to bring a large number of Russian forces back to the border via transport aircraft at any time.
Poroshenko has been invited by French President Francois Hollande to attend the 70th D-Day commemoration ceremonies on June 6, the Elysee Palace said.
Russian President Vladimir Putin is also invited to take part in the D-Day ceremonies, raising the prospect that the leaders could hold discussions then.
Even if international diplomatic efforts bear fruit, talks on the ground in Ukraine are complicated by divisions within the separatist movement.
Serhiy Taruta, the billionaire governor of Donetsk, told CNN Thursday he was in talks with pro-Russia separatist leaders in the region to try to calm the situation. But he suggested it was not proving easy.
"We are having dialogue, which is dragging out because they seem to have a constant rotation of their leaders, but I hope that in the final analysis we will reach an agreement and reconciliation to work together," he said.
Taruta has met with Poroshenko in Kiev, he said, adding that the President-elect will visit the Donetsk region "we hope in the first half of June."
The governor, speaking in Kiev, acknowledged that a Ukrainian military operation was under way in the Donetsk region, but he was unable to comment further.
CNN's Nick Paton Walsh reported from Donetsk, and Laura Smith-Spark wrote and reported in London. CNN's Barbara Starr, Hala Gorani and Boriana Milanova contributed to this report, as did journalist Francesca Humi.