Outgoing President Voronin is backing Prime Minister Greceanii's candidacy
Moldova's parliament has voted to postpone the second and final round of the presidential election until 3 June.
The 101-member assembly was due to vote on Thursday, but the ruling Communist Party voted to delay the poll, while the opposition refused to participate.
Last week, an opposition boycott left the Communists a vote short of electing their candidate, Zinaida Greceanii.
If the final round ends in deadlock the opposition will get its demand - a re-run of April's parliamentary election.
The result led to violent protests by opposition supporters, who alleged that the outcome was rigged.
Outgoing President Vladimir Voronin, the Communist Party leader and newly-elected speaker of parliament, has served the maximum two terms in office but wants to remain involved in affairs of state.
In his capacity as speaker, Mr Voronin proposed the postponement of the presidential election until next Wednesday and all 60 Communist deputies approved it. Within 10 minutes, the session was adjourned.
The leader of the Communists in the assembly, Maria Postoico, said the delay was due to the vote clashing with Ascension Day.
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"Today is a great religious holiday and it would be unacceptable for members of parliament to fight each other on this day," she said.
The move was condemned by Vlad Filat, the leader of the Liberal Democrats, one of the three centre-right opposition parties.
"The day's agenda had been approved. You can't change it because of a religious holiday," he told the parliament. "Society is expecting a solution."
The assembly had been due to vote on only two Communist Party candidates - Prime Minister Greceanii, Mr Voronin's choice to succeed him, and Stanislav Groppa - because the opposition parties refused to field their own candidates.
The opposition are boycotting the presidential election because they believe April's parliamentary poll was rigged.
In that election, the Communists gained 60 of the 101 votes in parliament - one short of the three-fifths majority needed to elect a president outright.
Violent clashes later erupted in the streets of the capital, Chisinau, after protesters stormed and set fire to public buildings.
International observers said the election was generally fair.
Mr Voronin's successor will lead the poorest country in Europe - where the average wage is just under $250 (£168) a month - and will inherit an unresolved conflict over the breakaway region of Trans-Dniester.