A poll by VPRC for Syntakton newspaper showed support for Prime Minister Antonis Samaras's New Democracy party at 29.5 percent, tied with the leftist opposition SYRIZA party.
Another survey by Metron Analysis for weekly newspaper Ependytis showed support for New Democracy at 27.8 percent versus SYRIZA's 28 percent.
The conservatives had trailed SYRIZA for months after the June election, but a January 11 poll by Public Issue showed they had pulled broadly level with the leftist opposition for the first time in months.
"The three-party ruling coalition seems to be regaining ground after the Eurogroup's decision in December secured the disbursement of a bailout tranche," Ependytis newspaper said.
"But it still faces a public opinion majority of 64 percent which feels the country is headed in the wrong direction."
The poll by VPRC put this figure at 67 percent.
Athens had been locked in talks with its international lenders for months on an austerity package to put its economic adjustment back on track and avert bankruptcy before aid was released in December.
According to both surveys, the far-right Golden Dawn party continued to rank third with 10.7 to 12 percent.
Support for the ruling coalition's junior partners, socialist PASOK and the Democratic Left party, ranged from 6.5-7.7 percent and 5.0-5.7 percent respectively.
The poll by Metron Analysis also showed 62 percent of Greeks think the country will manage to avoid bankruptcy.