Social Democrats leader Andrea Nahles said she wrote to other members of the coalition government to revisit Tuesday's agreement, which she said met with "widespread bewilderment" among Germans.
"We didn't create confidence, we lost confidence," she said of the deal that followed days of back-and-forth between those who supported the head of the BfV intelligence agency, Hans-Georg Maassen, and those who wanted him fired for appearing to downplay recent anti-migrant violence.
Merkel told reporters in Munich that she hopes to find a "viable solution" with her coalition partners over the weekend.
The German leader said it was important for her government to be able to concentrate fully on its job "in light of the many political challenges abroad and at home."
Maassen, who has also been criticized for his contacts with a far-right party, was backed by Horst Seehofer, the country's conservative interior minister. Seehofer agreed Tuesday to remove Maassen from the spy agency but then made him deputy minister - with a hefty pay rise.
An opinion poll published Friday by public broadcaster ARD showed Merkel's Union bloc receiving 28 percent of the vote and the Social Democrats getting 17 percent, compared with almost 33 and 20.5 percent respectively at last year's election.
The far-right Alternative for Germany party, meanwhile, has risen from nearly 13 percent last year to 18 percent in the same poll, which had a margin of error of up to 3.1 percentage points.
Copyright 2019 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.