"We think there's the possibility of change," Obama told reporters, answering an impromptu question about the significance of the elections.
"Ultimately the election is for the Iranians to decide," he said. "But ... you're seeing people looking at new possibilities. And whoever ends up winning the election in Iran, the fact that there's been a robust debate hopefully will help advance our ability to engage them in new ways."
The State Department was also speaking optimistically about Iran's election.
"It's a very positive sign that the people of Iran want their voices and their votes to be heard and counted," said Secretary of State Hillary Rodham Clinton. "Like many inside and outside Iran we are going to wait and see what the results are."
Obama has offered dialogue with Iran after a nearly 30-year diplomatic freeze between the two nations. He favors talks over Iran's nuclear program, which the United States and others fear is aimed at making weapons. Iran says it seeks reactors only for electricity.
State Department spokesman P.J. Crowley told reporters that the administration would continue its efforts to engage Iran no matter who wins the election.
"Our outreach to Iran is not dependent on a particular result," he said. "We look forward to engaging the new Iranian administration on the full range of issues before us."
A senior State Department official said later that the U.S. "would not be surprised if there is a run-off," noting the possibility that neither Ahmadinejad nor Mousavi would get the minimum 50 percent of the votes needed for an outright win due to the presence of a third candidate. The official spoke on condition of anonymity to discuss internal administration thinking.
In Brussels, Belgium Friday, Defense Secretary Robert Gates said he believes Washington is "interested in seeing the policies that the Iranian government follows."
"No matter who is elected, we would wait and see what kind of policies are followed by that person," he said. "It's less dependent on personalities than it is the policies that the leaders follow."
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