Greceanii was one vote short on Wednesday of receiving the necessary 61 votes in the 101-seat parliament and failed to be elected as president in the first ballot. The 41 opposition members of parliament walked out of the chamber to boycott the vote.
If the second vote, scheduled for May 28, fails, parliament must be dissolved and a new parliamentary election held.
The opposition, represented in parliament by the Liberal Party, the Liberal-Democratic Party and the Our Moldova alliance, has repeatedly stated its refusal to cooperate with the Communists inside or outside of parliament.
The Communists' victory in the April 5 parliamentary elections, which saw them gain 49.48% of the vote, sparked protests that turned violent in the capital, Chisinau.
Protests originally led by the opposition spiraled out of control when some 10,000 rioters broke into the presidential residence and parliament. Several hundred protesters and police were injured in the violence.
A number of opposition parties claimed major violations during the voting, alleging that some 400,000 people had been unlawfully registered to vote. However, observers from the Organization for Security and Co-operation in Europe gave their overall endorsement to the polls.