According to the ARD-Deutschlandtrend poll, Angela Merkel's conservative Christian Democrats (CDU) and the centre-left Social Democrats (SPD) have the same level of support.
A coalition of the SPD and Greens meanwhile would win 48 percent if an election were held this weekend – more than any other combination of parties and therefore enough to govern, the poll found.
Some 83 percent of voters, meanwhile, are unhappy with the coalition government of the CDU and the pro-business Free Democrats (FDP).
The poll put both the CDU and the SPD on 31 percent support – a two point loss for the CDU and a one point gain for the SPD compared with the previous month.
That compares with the 31.2 percent won by the CDU at the election in September last year and the 23.5 percent won by the SPD.
SPD boss Sigmar Gabriel told daily Berliner Zeitung the results reflected the “disastrous policies” of the coalition.
“But they also show that the SPD is on the right path,” he said.
Survey firm Infratest dimap polled 1,500 people of voting age between Monday and Wednesday this week.