The liberal interest group, known for its controversial political advertising, ran a full-page ad with that headline Monday, USA Today reported.
The ad has already sparked backlash from White House press secretary Tony Snow, who called the ad a "pre-emptive smear" on Petraeus and the Iraq war progress report he delivered on Monday.
Byron York of the conservative National Review Online wrote that MoveOn may have even embarrassed its own supporters this time.
"A number of Democrats are embarrassed, and even angered, by MoveOn's actions but are afraid to reveal the true extent of their feelings. MoveOn simply has too much fundraising clout," he said.
MoveOn will not apologize for the ad and continues to uphold its beliefs.
"We stand by our ad -- every major independent study and many major news organizations cast serious doubt on Petraeus' claims," said Eli Pariser, executive director of MoveOn.org Political Action Committee.
Couple mistakenly served bag of cash at McDonald's drive-thru
Beyonce flaunts bikini body, Blue Ivy in vacation pics