State televsion said a a young woman had died during the protests.
A presenter on Moldova 1 television said: "There are victims. One young woman choked to death from carbon monoxide poisoning in the parliament building."
Aisha Jung, a human rights worker in Chisinau, told Al Jazeera: "It started off with a peaceful demonstration in the central square. Everyone then walked peacefully to the presidential and parliamentary building.
"After about half-an-hour or an hour there they started to storm the presidential building with only a few policemen guarding it.
"They then went up the steps of the parliamentary building as well."
The recount decision came after the country's three main opposition leaders held talks with Vladimir Voronin, the president, and Zinaida Greceanii, the prime minister, following the storming of the parliament and presidential offices.
Dorin Chirtoaca, deputy head of the opposition Liberal party, said: "The protests will continue until a date is set for new elections.
"The protests are justified, their participants are calling for justice to be restored."
It was the second day of protests in the former Soviet state.
|Vladimir Voronin, Moldova's president, called for an end to the protests [EPA]
Earlier, Voronin had demanded an end to what he called the "bacchanalia" of protests.
He said: "Challenging the results of the election is no more than a pretext.
"We have no final election results. It is strange for us that the people organising this bacchanalia are in such a hurry.
"We cannot give any final assessment. The main thing is stop any continuation of the destabilisation sought by the organisers of this bacchanalia."
Grigory Karasin, Russia's deputy foreign minister, was quoted by Russia's Interfax news agency as saying: "We are following the situation with concern."
Javier Solana, the European Union foreign policy chief, urged all sides to refrain from violence.
He said: "I am very concerned over the situation in Chisinau. I call on all sides to refrain from violence and provocation.
"Violence against government buildings is unacceptable. Equally important is the respect for the inalienable right of assembly of peaceful demonstrators."
Earlier, protesters carrying Moldovan and European flags and shouting anti-Communist slogans had gathered outside the government buildings before making their way down Chisinau's main boulevard to the president's office.
"The election was controlled by the Communists, they bought everyone off," Alexei, a student, said.
"We will have no future under the Communists because they just think of themselves."
Voronin is not allowed to serve a third consecutive term, but has indicated that he wants to maintain control of the government after the election victory.
It is not clear what position he would take in the new administration.
The country's central election committee said on Monday that the Communists had secured about 50 per cent of the vote in Sunday's polls, with 98 per cent of the ballots counted.
They gained 61 parliamentary seats meaning that they do not need to consult parliament to choose a new president.