Eastern Ukraine slid deeper into anarchy Tuesday after pro-Russian protesters stormed and occupied the regional government headquarters in Luhansk, one of the largest cities in the region.

The occupations come amid escalating violence and lawlessness in two restive regions. On Monday at least five people were injured in the city of Donetsk, when baseball-bat wielding pro-Russians plowed into a gathering of about 2,000 unionist demonstrators. Yesterday, several dozen militiamen took over the city council building and a police station in Kostiantynivka, an industrial city in the Donetsk region. The armed men told journalists that they would occupy the buildings until a referendum on "federalization" – the devolution of power from the capital Kiev to the regions – is held.

Experts warn that the two eastern regions of Luhansk and Donetsk are in danger of slipping entirely out of Kiev's control. In much of eastern Ukraine local police have refused to obey orders from the central government or abandoned their posts, and a military operation aimed at reclaiming government buildings appear to have stalled.

"There is only one way to deal with this challenge, and that is through forceful measures," says Viktor Zamyatin, an analyst with the Razumkov Center, a leading Kiev think tank.

"Unfortunately, we do not have authorities who are strong enough," to carry out an effective crackdown, he adds.

Complicated views

Among residents in the restive areas, opinions over the political turmoil are complex. Ukrainian media have widely cited a recent poll that found big majorities in the largely Russian-speaking east opposed the seizure of government buildings. The mid-April survey by the Kiev International Institute of Sociology also found that only a minority supported Crimea-style reunification with Russia. Almost two-thirds of respondents said that Ukraine should remain a united country.

But the same poll also found that over half of respondents believed acting President Aleksandr Turchynov is "illegally occupying his post," while just under half thought the same about acting Prime Minister Arseniy Yatsenyuk. Both took power after the February overthrow of Russian-backed President Viktor Yanukovych.

And in the two restive regions where most building seizures and violence have occurred, the belief that Kiev's interim government is "illegitimate" was a massive 74 percent in Donetsk and 70 percent in Luhansk. Majorities also favored greater regional devolution and replacing Kiev-appointed governors with locally elected officials. That suggests most want to abolish the existing "unitary" state that concentrates power in Kiev.

These viewpoints may help to explain Kiev's relative restraint after threatening to use military force to "cleanse" the east of pro-Russian rebels. Instead it has opted for a more cautious approach: The Ukrainian Army is now trying to isolate pro-Russian strongholds, such as the town of Slovyansk in the Donetsk region. At the same time, it's working to cut off communications between rebel centers.

Russian role

The US ambassador to Ukraine, Geoffrey Pyatt, told journalists in Kiev Tuesday that Washington approves of this "prudent approach" that includes political outreach in eastern Ukraine as well as measured law enforcement measures.

But he put the blame for the unrest on Russia's ongoing military maneuvers near the Ukrainian border and alleged involvement of Russian agents in Ukraine. "This is a crisis that has its roots in decisions made by Russia," Mr. Pyatt said. "So it's Russia that will have to make the decisions that can deescalate the situation."

​Russia has consistently denied any involvement. Then again, Moscow also denied direct military involvement in the seizure of ​key buildings and transportation hubs in Crimea leading up to that territory's annexation by Russia last month. President Vladimir Putin cheerfully admitted later that Russian special forces had been "standing behind" local pro-Russian activists the whole time.

Still, much of the evidence that Russian forces are acting similarly in the eastern Ukraine has fallen short of the "smoking gun" standard.

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Defense Minister Sergei Shoigu told his US counterpart Chuck Hagel Monday that Moscow was ending its "military exercises" on Ukraine's border and returning troops to their barracks.

Mr. Shoigu reportedly said that the decision was made after "Ukrainian authorities declared they would not use regular military units against the unarmed [Ukrainian] population."