He said no official figures from the recount would be released ahead of a long weekend when mainly Orthodox Moldovans celebrate Easter.
Results from the original April 5 contest gave the Communists 49.48 per cent of the vote and 60 seats, one short of the number needed to ensure victory for their candidate when parliament chooses a new president.
Three opposition parties, broadly pro-Romanian and pro-European Union in outlook, scored a combined total of 35.34 per cent and won 41 seats.
They claim voting lists were swollen with 400,000 extra people who were either dead or living abroad.
Alexandru Tanase, vice-president of the Liberal Democratic party, complained that "a recount of fraudulent ballots will still yield a fraudulent result".
International observers, including the Organisation for Security and Co-operation in Europe, Europe's election watchdog, gave their overall approval to the original voting process.
The claims of election-rigging sparked large-scale protests on April 7, with up to 30,000 people demonstrating in Chisinau, the capital.
The president says the protests, in which some demonstrators ransacked the president's office and parliament, were part of a plot to seize power and were fomented by Romania, which shares a cultural and linguistic heritage with Moldova.
Romania denies the charges.
On Wednesday, Voronin called on legal bodies to proclaim an amnesty for most of the 200 protesters detained during the protests after international bodies accused Moldova of human rights violations.
The recounted results must be turned over to the Constitutional Court, which formally ordered the recount and must validate the figures, by April 22.
Voronin, in power since 2001, cannot run for a third term, but says he wants to keep a decision-making role.
Moldova, which lies between Ukraine and Romania, is officially Europe's poorest country.