Mr. Moussavi, who had called for the rally on Sunday but never received official permission for it, joined the crowd, as did Mohammad Khatami, the reformist former president. But the crowd was so vast, and communications had been so sporadic  the authorities have cut off phone and text-messaging services repeatedly in recent days  that many marchers seemed unaware they were there.

“We don’t really have a leader,” said Mahdiye, a 20-year-old student, who like many protesters declined to give a last name because of fears of repercussions. “Moussavi wants to do something, but they won’t let him. It is dangerous for him, and we don’t want to lose him. We don’t know how far this will go.”

The protesters said they would continue, with another major rally planned for Tuesday. But it was too soon to tell whether Ayatollah Khamenei’s decision to launch an inquiry, or the government’s decision to let the silent rally proceed, would change the election results. Many in the crowd said they believed that officials expected the protests to dissipate, as smaller protest movements did in 1999 and 2003.

Later on Monday, Mr. Moussavi said on his Web site that he was not optimistic that the authorities would overturn the election results. Demonstrators, though, expressed hopes that the tide had turned in their favor.

“Anything is possible,” said Hamid, a 50-year-old financial adviser. “If the people insist on this movement, if it continues here and in other parts of Iran, the pressure will build and maybe Ahmadinejad will be forced to resign.”

The police mostly stood on the sidelines on Monday. But after sunset, violence erupted after members of the Basij militia opened fire, leaving one dead and several others injured.

In Isfahan, south of Tehran, more violence broke out on Monday, with the police attacking a crowd of several thousand opposition protesters and rioters setting fires in parts of the city.