But its majority is too slim to push through their choice of president - who is elected by the assembly and not in a nationwide vote.
The communists, who were in power for eight years under former president Vladimir Voronin, remain the largest and only other party in parliament. They have so far succeeded in delaying the process of electing a new leader.
Parliament approved a motion on Thursday to delay the vote because there was only one candidate standing - communist defector Marian Lupu, who is the choice of the government and its Alliance for European Integration coalition.
The communists refused to propose a candidate.
Ion Plesca, chairman of the parliamentary committee overseeing the election, said: "There is precedent from 2000, when the constitutional court explained that the presidential election must be carried out on the basis of choice.
"We propose to parliament that it delays the vote to a later time so that it becomes legal."
No new date was set for the vote but under the constitution, a new president must be chosen by November 11.
Power struggle
Moldova has been suspended in a power struggle between the communists, who retained mostly good ties with former Soviet master Russia and prided themselves on policies of social protection, and the parties now in power, who hope to shift the country towards the European Union.
Earlier, Joe Biden, the US vice-president, said on a visit to neighbouring Romania that he backed the aims of the new government to move closer to Europe.
The EU has offered loans and talks on more co-operation.
The government coalition gets only two attempts in parliament to pass its choice for president. If it fails on the second vote, another snap parliamentary election will have to be called.
This was precisely the scenario that emerged after the communists won an election in April but also found they lacked votes to pass their choice for president. A snap election was called for July as a result.
Veteran communist Voronin is unable to stand for a third consecutive term and stepped down last month.