Petraeus, however, also now will be challenged with commanding a mission that the majority of Americans say is going badly, the Princeton, N.J.-based Gallup Poll conducted July 8-11 reported Tuesday.
The poll said Americans' opinions of the situation in Iraq improved during the time and afterward that Petraeus was the commander in Iraq.
Petraeus was appointed commander of U.S. and International Security Assistance forces in Afghanistan on June 23 shortly after President Obama removed Gen. Stanley McChrystal.
The majority of those queried said they think the U.S. effort in Afghanistan is going badly, which has been reflected in most Gallup polls in the last four years, Gallup said.
Most Americans, however, support the war. Only 38 percent say the U.S. was mistaken to have sent troops to Afghanistan in the first place, while 58 percent say it was not a mistake, Gallup reported.
Results for the poll were based on telephone interviews with a random sample of 1,020 adults, aged 18 and older, residing in the continental U.S., chosen through random-digit-dial sampling. The maximum margin of sampling error is between 4 and 5 percentage points.