Minister Alexis Tsipras led in Sunday's snap national polls, according to estimates based on the first official results released by the interior ministry.
The polls were the second conducted in the debt-laden country since January, Xinhua reported.
SYRIZA led by 35.5 percent of votes against 28 percent for the conservatives of the New Democracy (ND) party, with 30 percent of votes counted as of now.
Exit polls released earlier with the closing of the ballots by five polling firms for national broadcaster ERT and private channels gave SYRIZA 30-34 percent of votes versus 28.5-32.5 percent for ND.
Alexis Tsipras. File Pic/AFP
The two parties had secured 36.3 percent and 27.8 percent respectively in January's national polls.
Evangelos Meimarakis, ND's leader, admitted defeat and congratulated SYRIZA, speaking to media after the release of the exit polls.
If projections are reaffirmed by the final results expected on Monday, SYRIZA falls far short of securing the needed threshold to form a one-party government and therefore will be forced to seek alliances, as it happened after the January 25 elections that brought the Leftists in office for first time in Greece's modern history.
According to the estimate, the ultra-Right Golden Dawn remains the third largest party also in the new assembly, garnering 7.1 percent of votes up from 6.3 percent in January's ballot.
It was followed by the socialists of PASOK who were running with the Democratic Left this time. According to the projection, they win 6.4 percent of the vote and were trailed by the Communist party KKE which gets 5.5 percent.
The centrist Potami (River) secures about 4 percent of votes, the Right-wing Independent Greeks (ANEL) party which co-ruled with SYRIZA until August 3.7 percent of votes, and the Centre-Left Union of Centrists, a party which had marginal influence over the past two decades 3.4 percent.
The anti-bailout and pro-drachma Popular Unity party that was formed in late August by former SYRIZA MPs would most likely fail to enter the new assembly, garnering less than the three percent threshold needed under the county's electoral system.
Politicians, pollsters, political analysts and media commentators noted that Tsipras will most certainly seek to strike a coalition government with ANEL, but the two parties on their own will hold a slim majority.
Subsequently, the addition of a third junior partner -- perhaps PASOK-Democratic Left -- could not be excluded.
Commentators also stressed the high percentage of abstention as an index of the rising frustration of the Greek electorate with the conduction of six national elections in the past six years and the policies of most political parties.
According to the first estimate of the interior ministry, at least 45 percent of the 9.8 million eligible Greek voters did not show up at polling stations.
Despite disappointment over SYRIZA's u-turn this summer, most Greeks seem to have been persuaded that the Leftists could soften the impact of the forthcoming new round of austerity under the third bailout commitments in comparison to the Conservatives.
In January, the party won, pledging an outright end to austerity and bailouts. In the summer, faced with the threat of disorderly bankruptcy, Grexit, and after the closure of banks and the introduction of capital controls, SYRIZA signed a new harsh three-year bailout with Greece's international lenders.
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