New Democracy is 1.2 percent ahead of leftist SYRIZA opposition, according to the latest MRB poll published Thursday.
The survey, which was conducted after Monday's government reshuffle, puts the conservatives of Prime Minister Antonis Samaras on 22 percent and SYRIZA on 20.8 percent.
The neofascist Golden Dawn party is on 9.1 percent, followed by coalition partners PASOK on 6.1 percent, Independent Greeks on 5.5 percent, and the Communist Party (KKE) on 5.1 percent.
Democratic Left (DIMAR), which recently pulled out of Greece's coalition government, polls at 3 percent which is the threshold for entering Parliament.
The socialist party of Fotis Kouvelis on Wednesday sought to clarify its position on existing and forthcoming legislation, saying that it would offer its support on a case-by-case basis, backing government bills it agrees with and objecting to those it disagrees with.