Thousands of protesters, mostly students, also stormed the nearby parliament building, trashing a cafeteria, destroying office equipment and breaking windows. Part of the building was on fire and furniture was burned on the street.
A Romanian flag was hung over the entrance to the presidential residence, and the Moldovan flag on top of the residence was replaced with a European Union flag. Some protesters demanded reunification with Romania, waving Romanian flags and shouting "We are Romanians!"
The protesters also painted anti-communist slogans on the walls of the parliament building and a smoke-bomb was thrown from an upper floor of the building.
The protests 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 party's majority in parliament will give it the right to choose a new leader.
Parliament elects the president in the former Soviet republic, now Europe's poorest nation.
Police used water cannons as protests turned violent on Tuesday with rioters hurling stones and smashing windows in the capital. Soldiers had earlier used stun grenades to disperse rioters near the parliament building. At least 10 claps were heard in the crowd near parliament, and three ambulances were seen taking away injured people.
Earlier reports citing health officials said some 20 people, mostly rioters and bystanders, received minor injuries during the protest. Many people were walking around the city center watching the events unfold, some with their children.
The protests, which began peacefully, were initially led by Liberal Democratic Party leader Vlad Filat.
Filat warned on Tuesday that the opposition would go to any lengths, including the use of force, to have the votes from the election recounted. He later said protests would continue until new parliamentary elections are held.
"We will stay until new elections are held," the Liberal Democratic Party leader told demonstrators.
Speaking as the government gathered to address the riots, Voronin said there were no grounds to review the vote.
"Monitors during the April 5 parliamentary election in Moldova said no violations had taken place," the president said.
Voronin, one of only two communist leaders in Europe along with the Cypriot president, has served two consecutive terms and must step down under the constitution, although he has announced plans to stay in politics.