Bowing to a key demand of protesters who say the ruling Communist party rigged results, Voronin said in an official statement: "I am convinced that a complete recount of votes will become a major argument for maintaining political stability, peace and mutual trust in Moldova".
Violent opposition protests -- with crowds of students in the former Soviet republic denouncing alleged election fraud -- smashed their way into the parliament and set it ablaze on Tuesday. The authorities responded with a crackdown and mass arrests. The riots left more than 90 people injured and led to 200 arrests.
Moldova's Central Electoral Commission had announced the Communist Party lost its parliamentary majority after Sunday's elections, winning just under 50 percent of the vote and 60 seats in the 101-member parliament. That was revised down from an initial count of 61 seats.
This means the Communists don't have enough seats in parliament to appoint the president, but they still won the election.
The loss of the one seat means that the opposition, with 41 seats, have enough votes to block the naming of a successor to Voronin, who must step down after serving two terms in office.
More student protests
Some 200 anti-communist protestors gathered for a rally in the Moldovan capital, Chisinau, on Friday, calling for the resignation of the Communist government.
Standing in front of the government building, with many holding Romanian flags, the protesters chanted slogans such as "down with the communists" and "resignation." It was unclear whether they were aware of President Voronin's call for an election recount.
Prime Minister Zinaida Greceanii has urged students to stay away from the rally.
European Union urges normal relations with Romania
President Voronin had blamed Moldova's neighbour Romania for stirring up the riots and ordered the expulsion of the Romanian ambassador -- sparking an unprecedented diplomatic row with the new EU member.
Meanwhile, the European Union has urged Moldova to resume normal relations with Romania.
In a statement by the foreign ministers of France, the Czech Republic and Sweden, the 27-member bloc said it remains ready to work with Moldova in accordance with European values and principles. It stressed the need to maintain good ties with all its neighbors and urged that country to respect all constitutional freedoms.
Russia's slams Moldovan protests
Moscow has been closely observing the developments in Moldova.
Political analysts says the violent protests have triggered memories of street rallies in ex-Soviet republics Ukraine and Georgia that toppled pro-Moscow regimes, and raised fears that young Russian crowds might one day slip out of the Kremlin's control.
"The Moscow authorities are afraid of spontaneous mass protests in the regions...and for this reason Russian television is showing what is happening in an exclusively negative light," Dmitry Oreshkin, a Moscow-based political analyst told Reuters.
Foreign Minister Sergei Lavrov described the young Moldovan protesters who ransacked buildings as "pogrom-makers" set on destroying the country.
He's also warned the United States against forcing former Soviet republics to choose between an alliance with Washington and Moscow.