They seized the regional government's headquarters and prosecutor's office before opening fire with automatic weapons at the main police station.
Interim President Olexander Turchynov criticised local police for their "inaction" and "criminal treachery".
The US accused Russia of seeking to "change the security landscape" of Eastern and Central Europe.
By David SternBBC News, Kiev
The pro-Russian gunmen in Ukraine's east seem to be following a strategy of constant expansion and pressure on the Kiev government.
Hardly a day goes by without another incident. Just recently, official buildings in Kostyantynivka have been taken over, Western military monitors detained, peaceful demonstrators in Donetsk attacked, and now the regional administration building in Luhansk has been seized.
It is difficult to say what their ultimate goal is. Perhaps it is to keep government officials in Kiev on the defensive, forcing them to put out a number of fires at once, while others pop up throughout the region.
Or else it is simply to keep the situation unstable, in order to prevent the presidential election scheduled to take place on 25 May.
Or it could be just the opposite, as many in Kiev and throughout the country fear: to provoke the Ukrainians into a full crackdown, which would in turn spark a Russian invasion. The militants have called on Moscow to intervene on more than one occasion.
In a speech at the Atlantic Council in Washington, Secretary of State John Kerry told the Kremlin to "leave Ukraine in peace" and warned: "Nato territory is inviolable we will defend every single inch of it."
In other developments on Tuesday:
Moscow has said it has 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 30km (20 miles) from the Russian border, had been targeted.
But on Tuesday afternoon, hundreds of people shouting "Russia, Russia" gathered outside the headquarters of the regional government to demand a referendum on greater autonomy.
A group of men armed with sticks and metal bars broke into the building. They pulled down the Ukrainian flag flying from the roof and replaced it with a Russian tricolour and the flag of Donetsk People's Republic.
Crowds of pro-Russia activists then overran the building housing the prosecutor's office before attacking the headquarters of the interior ministry's police force.
Hours later, an AFP news agency journalist reported that officers had abandoned the police station and been taken away in buses, as an angry crowd shouted at them to "Go home".
Activists also went into a regional television station, but decided not to take it over after they were allowed to make a live broadcast.
Following the takeovers, President Turchynov demanded the dismissal of the police chiefs in Luhansk and the other eastern city of Donetsk.
"The overwhelming majority of law enforcement bodies in the east are incapable of fulfilling their duty to defend our citizens," he said.
Pro-Russia activists control much of the neighbouring Donetsk region.
Sanctions
By Daniel SandfordBBC News, Moscow
Sanctions screw is tightened
Eastern Ukraine, which has a large Russian-speaking population, was a stronghold for former President 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 Organisation for Security and Co-operation in Europe (OSCE) seized last week.
On Tuesday evening, the self-styled "mayor" of the town of Sloviansk, where the observers are being held, said "good progress" had been made at talks with OSCE representatives.
Vyacheslav Ponomaryov had earlier warned that they would only be released if the EU dropped its sanctions against separatist leaders.
Earlier, the EU published a fresh list of 15 individuals facing travel bans and asset freezes.
It included the chief of the Russian General Staff, the head of Russian military intelligence, and a Russian deputy prime minister, as well as separatist leaders in Crimea, Luhansk and Donetsk.
On Monday, the US announced sanctions against seven individuals and 17 companies it said were linked to President Putin's "inner circle".
President Putin warned that new sanctions might have an impact on the operations of Western companies in Russia.
"If this continues, we will of course have to think about how they work in the Russian Federation, including in key sectors of the Russian economy such as energy," he said, adding that there were "neither Russian instructors, nor special units, nor troops" in Ukraine.
US Treasury Secretary Jack Lew said the sanctions, first imposed by Washington and Brussels after Crimea was annexed, had so far caused "a quite substantial deterioration in Russia's already weak economy".
Pro-Russia activists have stormed several official buildings in the eastern Ukrainian city of Luhansk.