WASHINGTON -- President Obama on Monday said Iranian voters have a right to feel that their ballots matter and urged the investigation into vote-rigging allegations to go forward without additional violence.

Obama said reports of violence that followed Iranian elections trouble him and all Americans. Peaceful dissent should never be subject to violence that followed weekend elections that gave President Mahmoud Ahmadinejad a second term, he said.

"It would be wrong for me to be silent on what we've seen on the television the last few days," Obama told reporters at the White House.

Obama said he had no way of knowing whether the results are valid -- the United States, he noted, had no election monitors in the country -- but he added that it is important that the voters' choices be respected.

Hundreds of thousands marched in central Tehran. Gunfire from a pro-government militia killed one man and wounded several others while the government cracked down on dissent. An Associated Press photographer saw at least one demonstrator killed and several others with what appeared to be serious injuries.

The march came as Iran's most powerful figure, Ayatollah Ali Khamenei, ordered an investigation into vote rigging against reform leader Mir Hossein Mousavi.

"I am deeply troubled by the violence I've been seeing on TV," Obama said.

Obama said he would continue to engage the Middle East nation, even if Ahmadinejad's re-election is upheld.

Obama said the United States must work with the country to prevent a nuclear arms race in the region. He emphasized that he disagrees with Ahmadenijad's "odious" beliefs and said the United States has serious disagreements with Iran's foreign policy.

Yet, he said, the United States has a broader interest in stopping Iran from developing nuclear weapons or exporting terrorism.

The president was careful not to wade too deeply into Iran's domestic politics, recognizing "sometimes, the United States can be a handy political football." He said it's up to Iran to determine its own leaders but that the country must respect voters' choice.

However, Obama praised protesters and the nation's youth who question results that showed Ahmadinejad winning a second term in a landslide.

"The world is watching and is inspired by their participation, regardless of what the ultimate outcome of the election was," he said.

Obama's remarks came at the end of an Oval Office meeting with Italian Premier Silvio Berlusconi.