The Forsa institute put the poll's margin of error at 2.5 percentage points, meaning Merkel's conservative CDU/CSU bloc and the SPD are in a neck-and-neck race.
Both Merkel, who will seek a fourth term as chancellor, and Schulz are hoping to end their parties' current 'grand coalition' and to form a new government with smaller allies.
The poll showed the anti-immigrant Alternative for Germany (AfD) down 2 percentage points at 7 percent, which is the lowest level of support in that poll since November 2015.
The far-left Linke gained one percentage point to reach 8 percent, making it the third-strongest party. The Greens stood at 7 percent and the business-friendly Free Democrats (FDP) at 6 percent -- above the 5 percent threshold needed to enter parliament.
The poll of some 2,500 voters was carried out between March 20-24. The weekly poll mirrored the results of a monthly survey by the Allensbach institute for newspaper Frankfurter Allgemeine Zeitung which were published on Tuesday.
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