Protesters clashed with police, waved Russian flags and called for a referendum on independence from Ukraine.
Ukraine’s acting President Oleksandr Turchynov called an emergency security meeting.
The unrest comes amid tensions between Russia and Ukraine over the removal of pro-Moscow President Viktor Yanukovych and Russia’s annexation of Crimea.
In Donetsk, about 50 people broke away from a rally of about 2,000 people in the city centre, and got past a police cordon to enter the regional administration building.
The activists shouted “Donetsk is a Russian city” and raised Russian flags above the building.
Some called for the region to have a referendum on the region’s independence from Ukraine.
A similar referendum held in the Crimean peninsula in March led to Russia’s annexation.
In Luhansk, near the Russian border, dozens of demonstrators stormed the offices of the state security agency.
Ukrainian media said protesters pelted the building with eggs, a smoke grenade and a firebomb.
Similar incidents were later reported in Kharkiv.
Russia’s President Vladimir Putin has vowed to protect Russian-speaking people in eastern Ukraine.
President Oleksandr Turchynov has cancelled a diplomatic trip to Lithuania to deal with the unrest, according to his press service.
The statement said Oleksandr Turchynov would hold an emergency meeting with the heads of security services.
Tensions are running high between Ukraine and Russia, with thousands of Russian soldiers still said to be deployed along the border.
Viktor Yanukovych was forced from office in February, following months of street protests.
The new administration has faced continuing opposition from Ukraine’s Russian-speaking regions, particularly in the east of the country.
Russia has said it will defend the rights of ethnic Russians in Ukraine – which it claims are under threat under the new government – but has said it will not send troops into the rest of the country.
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