The parties also agreed to do everything possible to stop the violence, which has left hundreds of people injured, although opposition leaders said they had lost control of the situation.
The protests in Chisinau began on Monday, following the Communist Party's victory in Sunday's parliamentary polls, but turned violent on Tuesday.
Communist President Vladimir Voronin is due to step down on May 7, but the Communist Party won just enough seats in parliament to be able to elect a successor without the votes of any other party.
Thousands of anti-communist protesters seized the presidential residence and the nearby parliament building. Police have withdrawn from both buildings, parts of which were on fire, and rioters were looting offices and burning furniture in the street.
They have also painted anti-communist slogans on the walls and hung Romanian and EU flags from the presidential residence.
A police source said earlier that "some 400 out of 800 members of the inter-service force that was guarding the buildings of the presidential administration and the parliament were injured and sought medical assistance as a result of the protesters' attacks."
The Moldovan Central Election Committee pledged to recount the ballots within 10 days.
Earlier in the day, Voronin declared that there were no grounds for a review of the results, saying that election monitors had observed no violations.
The European Union's foreign policy representative, Javier Solana, expressed concern on Tuesday about events in Chisinau, urging the sides to refrain from violence. He added that the elections had met international standards.
Terry Davis, the secretary general of the Council of Europe, also condemned the violence and said the polling was carried out in line with international norms.
"Council of Europe and other international observers noted several shortcomings, which will have to be improved before the next elections, but they did not challenge the overall results," he said.
"Some people may not be happy with the outcome, but accepting defeat is a part of the democratic process. As to any specific allegations of electoral irregularities, these should be dealt with in the court not in the street," Davis continued.
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.