Some 53 percent of those polled said they wanted Merkel to remain chancellor while 38 percent backed her biggest challenger in next year's general election, Peer Steinbruck, Der Spiegel reported Monday.
The survey found Merkel's Christina Democratic Union party 9 points ahead of its center-left rival, the Social Democratic Party, 39 percent to 30 percent.
Even so, nearly 70 percent of Germans say the Merkel government favors special interests to the detriment of the public good, found a "government monitor" survey by polling group Forschungsgruppe Wahlen.
Only 24 percent said the public good topped the government's list of priorities.
Some 65 percent said the German government was "not at all" or "not very strongly" interested in dealing with future problems.
Merkel's shift toward renewable energy was slipping as well, the survey found. Some 42 percent said they supported the chancellor's stand, down 10 percent from July.
The coalition party of Vice Chancellor Philipp Rosler, the FDP, has crippled the success of Merkel's administration, the survey said. Only 15 percent considered him effective.
Support for the FDP has slid to less than the 5 percent minimum necessary to run for election to the Parliament, a separate survey indicated.
The number of people surveyed and the margins of error were not reported.