Even while supporting the president’s approach, senior members of the administration, including Vice President Joseph R. Biden Jr. and Secretary of State Hillary Rodham Clinton, would like to strike a stronger tone in support of the protesters, administration officials said.

Other White House officials have counseled a more cautious approach, saying harsh criticism of the government or endorsement of the protests could have the paradoxical effect of discrediting the protesters and making them seem as if they were led by Americans. So far, Mr. Obama has largely followed that script, criticizing violence against the protesters, but saying that he does not want to be seen as meddling in Iranian domestic politics…

Many Iran experts lauded Mr. Obama’s measured stance just after the election. But some of that support evaporated on Tuesday when he said there was not much difference between Mr. Ahmadinejad and Mr. Moussavi…

“Up until now, the president had very thoughtfully calibrated his remarks on Iran, but this was an uncharacteristic and egregious error,” said Karim Sadjadpour, an Iran expert with the Carnegie Endowment for International Peace. “People are risking their lives and being slaughtered in the streets because they want fundamental change in the way Iran is governed. Our message to them shouldn’t be that it doesn’t make much difference to the United States.”