Thousands of young protesters thronged Chisinau, fighting police and ransacking parliament, in protest at the results of Sunday's election.
Official results gave the ruling Communists about 50% of the vote in the Romanian-speaking ex-Soviet republic.
International observers said the vote appeared to have been fair, though one told the BBC she had her doubts.
President Voronin, a Communist, was quoted by Russian agency Interfax saying: "We know that certain political forces in Romania are behind this unrest. The Romanian flags fixed on the government buildings in Chisinau attest to this."
Earlier he described the violence as "a coup d'etat".
Some of the protesters on Tuesday had called for the unification of Moldova with Romania, its bigger neighbour.
Russia's foreign ministry said there was a plot aimed at undermining "the sovereignty of Moldova".
Summoned on Twitter
UN chief Ban Ki-moon called for calm and EU foreign policy chief Javier Solana said violence against government buildings was "unacceptable".
The streets of Chisinau were quiet on Wednesday morning. Protesters had left the scene of the rioting on Tuesday night, and police retook control of parliament.
But opposition leaders said protests would continue.
Vlad Filat, leader of the Liberal Democratic Party, called the demonstrations "a spontaneous action by protesting young people".
He said the opposition had tried to prevent excesses, like the attacks on parliament, but said: "We are not scared of arrests or intimidation. The people do not want to live like this and want to live free and without fear."
Word of the demonstrations was spread by text message, via the internet, and on social networking tools.
"We sent messages on Twitter but didn't expect 15,000 people to join in. At the most we expected 1,000," Oleg Brega, of the activist group Hyde Park told the Associated Press news agency.
Chisinau Mayor Dorin Chirtoaca, a member of the Liberal Party, said: "The elections were fraudulent, there was multiple voting."
The opposition have called for ballots to be recounted or the vote to be reheld - a request rejected so far by the government.
A report by the Organisation for Security and Co-operation in Europe on Sunday's vote gave a mostly positive assessment of the poll.
But a British member of the OSCE's observation team questioned that conclusion.
Baroness Emma Nicholson said she found it "difficult to endorse the very warm press statement" from the head of the OSCE.
"The problem was that it was an OSCE report, and in the OSCE are, of course, the Russians, and their view was quite different, quite substantially different, for example from my own," she told BBC News.
She said she and other observers had a "very, very strong feeling" that there had been some manipulation, "but we couldn't find any proof".
Moldova, sandwiched between Romania and Ukraine, is the poorest country in Europe, where the average wage is just under $250 (£168) a month.
The people speak Romanian and the country shares many cultural links with Romania. However it was annexed by the Soviet Union in World War II and gained independence in 1991.
There remains an unresolved conflict with the breakaway region of Trans-Dniester, which has run its own affairs, with Moscow's support, since the end of hostilities in a brief war in 1992