A few dozen men, some reportedly armed with metal bars, smashed windows and doors to break into the building.
Activists shouting “Referendum Russia” later flew a Russian flag over it.
Earlier, Russia criticized sanctions imposed by the US and EU on individuals and companies over their alleged actions aimed at destabilizing Ukraine.
Deputy Foreign Minister Sergei Ryabkov said the US had “essentially lowered an <<Iron Curtain>>” by targeting Russia’s high-tech sector.
The EU, he added, had proved that it was “under Washington’s thumb”.
Russia’s Deputy PM Dmitry Rogozin meanwhile warned that if the sanctions affected its rocket-building sector, US astronauts on the International Space Station (ISS) might be “exposed”.
Sergei Ryabkov also stressed that Russia had no intention of invading eastern Ukraine, where pro-Russia activists have seized government buildings in more than a dozen towns and cities.
Until now, only the local office of the State Security Service (SBU) in Luhansk, a city of 465,000 people less than 20 miles from the Russian border, had been targeted.
But on Tuesday afternoon, hundreds of people gathered outside the headquarters of the regional government to demand a referendum on granting greater autonomy to the east.
A group of men armed with sticks and metal bars broke into the building, whose entrances were not protected by police. They then pulled down the Ukrainian flag flying from the roof and replaced it with a Russian one, and opened the main entrance to the crowd.
Inside the building’s courtyard, they found security personnel in riot gear massed in a defensive position. There was a stand-off, but no violence.
“The regional leadership does not control its police force,” Stanislav Rechynsky, an aide to the interior minister in Kiev, told Reuters news agency.
“The local police did nothing.”
Stanislav Rechynsky added that the government had information to suggest that the separatists would now seize the local television centre.
Eastern Ukraine, which has a large Russian-speaking population, was a stronghold for former President Viktor Yanukovych before he was overthrown by protesters in February.
The interim government has rejected the pro-Russian activists’ demands for greater autonomy, fearing they could lead to the break-up of the country or more regions being annexed by Russia, as happened with Crimea last month.
Pro-Russian activists continue to detain some 40 people, including seven military observers linked to the Organization for Security and Co-operation in Europe (OSCE) seized last week.
The self-styled “mayor” of the town of Sloviansk, where the observers are being held, has said he will discuss their release only if the EU drops sanctions against separatist leaders.
On Tuesday, the EU published a fresh list of 15 individuals facing travel banks and asset freezes.
It included General Valery Gerasimov, chief of the Russian General Staff, and Lt. Gen. Igor Sergun, identified as the head of the Russian military intelligence agency, the GRU.
Russian Deputy PM Dmitry Kozak and pro-Russian separatist leaders in Crimea and in Luhansk and Donetsk were also named.
On Monday, the US announced sanctions against seven individuals and 17 companies it said were linked to President Vladimir Putin’s “inner circle”.
The US and EU first imposed visa bans and asset freezes on a number of senior Russian officials and companies after Crimea was annexed.
US Treasury Secretary Jack Lew said the sanctions had so far caused “a quite substantial deterioration in Russia’s already weak economy”.
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