Syriza was supported by 23 percent of those polled, with the conservative New Democracy party second on 19.5 percent, according to the survey, carried out by pollsters ProRata and published in Friday`s Efimerida Ton Syntakton newspaper.
The previous ProRata poll in early July showed a wider gap in Syriza`s favor, putting the party on 26 percent compared with 15 percent for New Democracy.
Based on the survey, 64 percent of Greeks believe Tsipras`s move to call snap polls was wrong, while 68 percent agreed that Greece must stay in the euro zone at any cost, even if that meant further austerity.
"The answers to these two questions lead to the conclusion that early elections may cost the (former) prime minister and Syriza," the newspaper said.
Early elections are expected on Sept. 20, a date the president is likely to confirm later on Friday after a caretaker government is sworn in.
Tsipras abruptly resigned last week days after clinching an 86 billion euro ($97.2 billion) bailout package from European and International Monetary Fund lenders, hoping to crush a rebellion by far-left lawmakers and tighten his grip on power.
Popular Unity, the party formed last week by Syriza rebels who oppose the bailout, was backed by 3.5 percent in Friday`s poll - just above the 3 percent threshold needed to enter parliament.
But the Independent Greeks, the ally in Tsipras` former coalition government, scored just 2 percent, meaning Syriza would be forced to seek another coalition partner.
Tsipras this week ruled out cooperating with the main pro-euro opposition parties - New Democracy, the Socialist PASOK and the centrist To Potami. The poll`s result suggested that, in that event, the country would face a second round of elections.
One third of those who supported Tsipras` party in the January 2015 elections that took him into office said they were unsure if they will do so again, the poll said.
It also showed 25.5 percent of voters were still undecided, making them the biggest bloc.
More about:
