In an appearance Wednesday on ABC's "Good Morning America" to promote his new book, Rove came down on Obama for participating in the debate on what he said many consider should be left as a local issue.
Obama said Friday Muslims have the same constitutional right as others "to build a place of worship and a community center on private property in Lower Manhattan, in accordance with local laws and ordinances." He said Saturday he "was not commenting and I will not comment on the wisdom of making the decision to put a mosque there."
The proposed project is near where the World Trade Center towers once stood.
"The president was better to have signaled a tone of respect for Islam on Friday night without engaging in a local controversy that he previously avoided and after Saturday morning, that he said he'll avoid again," said Rove -- a top adviser to former President George W. Bush who currently works as a commentator for Fox News Channel.
"He did real damage to America's standing in the world by this inconsistent and incoherent answer that he gave Friday night with a different answer on Saturday morning," Rove said.