The protests in Chisinau began on Monday, following the Communist Party's victory in parliamentary polls. Communist President Vladimir Voronin is due to step down on May 7, but the Communist Party's majority in parliament will give it the right to choose a new leader.
At midday, around 5,000 demonstrators left the capital's central square and headed toward parliament and the presidential residence.
Some of the protesters are also demanding reunification with Romania, waving Romanian flags and shouting "We are Romanians!"
A RIA Novosti correspondent said rioters have broken into parliament, and are burning furniture from the building on the street outside. They have also painted anti-communist slogans on the walls. A smoke-bomb has been thrown from an upper floor of the building.
Police have been using water cannons to disperse the rioters and prevent demonstrators from entering the presidential residence. The Interior Ministry insists that the situation is under control.
"The situation is under police control, and will remain under their control," ministry spokeswoman Alla Meleka told RIA Novosti.
Several people including police officers have been injured by rocks being thrown by rioters.
Voronin, one of only two communist leaders in Europe along with the Cypriot president, has served two consecutive terms since his election in 2001. Under the constitution, he is banned from seeking a third consecutive term.
The protests, which began peacefully, were initially led by Liberal Democratic Party leader Vladimir Filat.
Filat warned on Tuesday that the opposition would go to any extremes, including forceful means, to have the votes from the election recounted.
