Mr Turchynov said the goal was now to prevent the unrest spreading.
Activists have seized scores of government buildings and taken hostages including international monitors.
Mr Turchynov also said Ukraine was on "full combat alert", amid fears Russian troops could invade.
"I would like to say frankly that at the moment the security structures are unable to swiftly take the situation in the Donetsk and Luhansk regions back under control," he said during a meeting with regional governors.
He admitted security personnel "tasked with the protection of citizens" were "helpless".
"More than that, some of these units either aid or co-operate with terrorist groups," he said.
Mr Turchynov added: "Our task is to stop the spread of the terrorist threat first of all in the Kharkiv and Odessa regions."
'Recession' warning
The acting president said that the tens of thousands of Russian troops stationed just over the border meant that "the threat of Russia starting a war against mainland Ukraine is real".
Russia, which annexed the Crimea region from Ukraine last month, has said it has no plans to invade the east.
President Vladimir Putin has insisted there are "neither Russian instructors, nor special units nor troops" inside Ukraine.
However, Moscow has also warned that its soldiers are ready to act if Russian interests are threatened.
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