"It is up to Iranians to make decisions about who Iran's leaders will be," Obama told reporters at the White House. "We respect Iranian sovereignty and want to avoid the United States being the issue inside of Iran."
"Having said all that, I am deeply troubled by the violence I've been seeing on television," he added. "I think that the democratic process, free speech, the ability of people to peacefully dissent - all those are universal values and need to be respected."
The United States and Iran have had no diplomatic relations since 1980, and their historic ties are strained from a U.S.-backed coup in 1953 and Washington's longtime support of Shah Mohammed Reza Pahlavi, who came to power in the coup. Pahlavi was overthrown in the 1979 Islamic revolution that established the current Iranian government, which came to power calling the Washington the "Great Satan."
Official results of Friday's vote showed hardline incumbent President Mahmoud Ahmadinejad winning a second term by a 2-to-1 margin over challenger Mir Hossein Moussavi, a former prime minister. Obama did not take a position on the claims of fraud that have brought Moussavi's supporters onto the streets, but he said, "The Iranian people and their voices should be heard and respected."
"Whenever I see violence perpetrated on people who are peacefully dissenting, and whenever the American people see that, I think they are rightfully troubled," he said. "I think it would be wrong for me to be silent about what we've seen on the television over the last few days."
Obama said those "who put so much hope and energy and optimism into the political process" should know "that the world is watching and inspired by their participation, regardless of what the ultimate outcome of the election was."
An administration official, speaking on condition of anonymity, said the lack of election monitors on the ground has made verifiable information difficult to obtain. But he said some elements of the results - including Ahmadinejad's reported win in Moussavi's home province - have raised "early indications" of fraud.
Iranian officials have denied the claims. The country's Guardian Council, which oversees elections, has said it would investigate, but Moussavi told supporters in an online statement Monday that the council had not remained neutral and "I don't have any hope in them."
An Iranian official who asked to remain unidentified told CNN that Moussavi was not popular in his hometown of Tabriz, in the country's north, and said allegations that the Guardian Council was in Ahmadinejad's corner are "unfair and unfounded."
– CNN Correspondent Brian Todd contributed to this report.
Updated: 8:15 p.m.