The poll showed Syriza set to win 25 percent of votes, just behind New Democracy on 25.3 percent. More than one in 10 voters remained undecided, meaning the final outcome is far from certain.
Vassiliki Thanou, an anti-austerity advocate who has argued against wage cuts for judges and court officials, will be sworn in as the country’s first female prime minister.
Syriza says it is aiming for an outright majority, although the strength of its support is unclear due to a lack of surveys by leading pollsters in the past month.
The prime minister hopes to strengthen his hold on power in snap elections after seven months in office in which he fought Greece’s creditors for a better bailout deal but had to cave in.
Tsipras is hoping to quell a rebellion in his leftist Syriza party and seal support to implement a tough bailout program.
A government spokeswoman said drafting of the bailout accord, which requires approval from Greece’s fractious parliament, would start on Wednesday.
Tsipras faces a tough Syriza central committee session on Thursday with many activists angered by his acceptance of bailout terms more stringent than those voters rejected in a July 5 referendum.
Any hope of a fresh start in fraught relations between Greece’s leftist government, purged of its most radical members, and the institutions representing its creditors, appeared to be dashed by the flurry of assertions and rebuttals.