The offensive occurred a day after the start of European-brokered talks which have yet to draw in the warring sides.
Turchynov told lawmakers that government forces attacked an insurgent base in the city of Slavyansk and another one in nearby Kramatorsk, about 95 miles west of the Russian border.
Ukraine's defense ministry said there were no casualties while the army took three insurgents captive, including one who was armed with a rocket-propelled grenade launcher.
AP journalists in Slavyansk heard bursts of automatic gunfire overnight, but details of Turchynov's statement couldn't be independently confirmed.
The situation was quiet during the day Thursday, and there has been no comment from the insurgents to the claims made by Turchynov.
Turchynov didn't describe the insurgents' bases or give any further details.
Both government troops and insurgents have checkpoints around Slavyansk and Kramatorsk.
Some previous Ukrainian claims of successful operations have proved to be exaggerated.
Insurgents, who have seized government buildings across eastern Ukraine and fought the Ukrainian military, declared two eastern regions independent following Sunday's referendum, which was dismissed as a sham by the Ukrainian government and the West.
The Organization for Security and Cooperation in Europe, a trans-Atlantic security group, put forward a "road map" calling for national dialogue as a first step toward resolving the escalating tensions.
The first round of talks in Kiev produced no visible result as the government has confirmed its refusal to sit down with representatives of the insurgents.
In the east of Ukraine, insurgents said they hadn't been invited to the Kiev round table and said that talks should be held in Donetsk.
One of the leaders of the insurgency, Denis Pushilin, said it should focus on prisoners exchange and the pullout of the government forces, whom he called "occupation troops."
Some present at the meeting pushed for separatist representatives to be included, the Wall Street Journal reported.
"Without their participation, the round tables will just be declarative," said Nestor Shufrych, a senior lawmaker from the Party of Regions that used to back ousted President Viktor Yanukovych.
Ex-President Leonid Kuchma said he hadn't expected the meeting to produce an immediate result.
"We can't solve the problems in a day," he said, according to the Journal.
"We want to make a hot situation just warm."
The next session of the talks is expected on Saturday, but the government hasn't made any specific commitments.
In Moscow, Russian Foreign Ministry spokesman Alexander Lukashevich what he called a "stubborn reluctance of the authorities in Kiev to launch a real process of national reconciliation."
Commenting on Moscow's attitude to the Donetsk insurgents' appeal to join Russia following the referendum, Lukashevich made it clear that the Kremlin has no immediate intention to do so, saying that the priority is to encourage talks between the government and its foes.
"Russia has actively pushed for launching a broad national dialogue between Ukrainians about ways of forming the future of Ukrainian state," Lukashevich said.
At the meeting in Kiev, Ukraine's interim president, Turchynov, said the government was ready to hand more powers to the regions and to hold talks with everyone except for "those who with weapons in their hand try to wage war with their own country," The Wall Street Journal reported.
Source: FOX News