Acting President Oleksandr Turchynov said his government's goal now was to prevent the agitation from spreading to other territories in the sprawling nation of 46 million people.
His interim government in Kiev and Western governments have accused Moscow of orchestrating the turmoil in eastern Ukraine, which borders Russia. The United States and the European Union rolled out new economic sanctions against Russia this week but Moscow has remained unbowed, denying its role in the unrest.
Turchynov spoke hours after pro-Russia gunmen seized more administrative buildings in eastern Ukraine.
Kiev city authorities, meanwhile, announced unexpected middle-of-the night security drills running from Wednesday night into Thursday morning by the state guard service. That could alarm the eastern insurgents who favor more independence or even separatism, but also could be aimed at reassuring Ukrainians unsettled by Turchynov's admission of impotence in the east.
At a meeting in Kiev, Turchynov laid out the central security challenge facing Ukraine, instructing regional governors to try to prevent the threat in the east from overtaking central and southern regions.
"I will be frank: Today, security forces are unable to quickly take the situation in the Donetsk and Luhansk regions under control," Turchynov said. "The security bodies ... are unable to carry out their duties of protecting citizens. They are helpless in those matters. Moreover, some of those units are either helping or cooperating with terrorist organizations."
He said "mercenaries and special units" were attacking eastern Ukraine.
"That is why I am stressing our task is to stop the spread of the terrorist threat, first of all in the Kharkiv and Odessa regions," Turchynov was quoted as saying by the Interfax news agency.
The mayor of Kharkiv, who had been credited with keeping Ukraine's second-largest city calm, was shot in the back earlier this week.
Turchynov said the threat of a Russian invasion was real and urged the creation of regional self-defense units throughout the country, according to the Interfax news agency. Russia has placed tens of thousands of troops near the border with Ukraine and has annexed the Black Sea peninsula of Crimea.
Yulia Torhovets, a spokeswoman for the Kiev city government, would not provide any details about the drills, saying only that the city made the announcement to keep residents informed.
"We didn't want people to get scared when they see combat equipment," Torhovets told The Associated Press. "We didn't want anyone to panic."
Some Ukrainians were appalled by the loss of control over the country's eastern regions and accused the central government of reacting too slowly.
"In a normal society, when Oleksandr Turchynov admits the fact that the authorities do not control the situation in the east of the country, that's grounds for resignation. And not just from him, but all the security forces," Valeriy Kalnysh, the former editor of the now-defunct Kommersant Ukraine daily, wrote on Facebook. "But can we afford this now? .... And is it the right move in the conditions of an undeclared war with Russia?"
Former prime minister and presidential candidate Yulia Tymoshenko urged Ukrainians to join a resistance force that she was creating that would act in coordination with the army.
"Ukraine is under attack. Russia has begun an undeclared war against our country in the east," Tymoshenko said in a statement Wednesday. "I call upon all patriots who have ever participated in military operations to join us immediately.
Ukraine is holding a presidential election on May 25, and Tymoshenko is among several top candidates.
In eastern Ukraine, insurgents wielding automatic weapons took control and hoisted an insurgent flag on top of the city council building Wednesday morning in the city of Horlivka in the Donetsk region. They also took control of a police station in the city, adding to another police building they have controlled for several weeks.
An Associated Press reporter saw armed men guarding the city council building in Horlivka and checking the documents of those entering. One man said foreign reporters would not be allowed in and threatened to arrest those who didn't obey. Similar guards were also seen outside the city's police station.
The insurgents who now control buildings in about a dozen cities in eastern Ukraine are demanding broader regional rights as well as greater ties or outright annexation by Russia. The militiamen are holding some activists and journalists hostage, including seven observers from a European security organization.
In Luhansk, one of the largest cities in eastern Ukraine, gunmen in camouflage uniforms maintained control of several government offices they seized Tuesday. In Donetsk, insurgents added the local tax agency office to the list of buildings they have seized.
Dzhavad Iskanderov, a spokesman for the insurgents, told the AP the tax building was seized to prevent nationalists and other pro-Kiev forces from seizing the weapons inside.
Eastern Ukraine, which has a large Russian-speaking population, was the heartland of support for Viktor Yanukovych, the ousted president who fled to Russia in February. The government that replaced him in Kiev has resisted the insurgents' demands, fearing they could lead to a breakup of the country or more regions being annexed by Russia.
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