Official media made no mention of clashes or arrests and state television said "tens of millions of people" attended rallies in support of the revolution across the country of 70 million.
President Mahmoud Ahmadinejad told a vast, flag-waving crowd of government supporters in central Tehran's Azadi (Freedom) Square that Iran was now able to enrich uranium to more than 80 percent purity, coming close to levels experts say would be needed for a nuclear bomb, although he again denied it had any such intention.
"The Iranian nation is brave enough that if one day we wanted to build nuclear bombs we would announce it publicly without being afraid of you," Ahmadinejad said, addressing Iran's Western opponents.
But he told the crowd: "When we say that we don't build nuclear bombs, it means that we won't do that because we don't believe in having it."
State television showed live footage of hundreds of thousands of people, some carrying Iranian flags and pictures of supreme leader Ayatollah Ali Khamenei, walking to the square.
An opposition website, Iran's Green Voice, said security forces fired shots and tear gas at supporters of opposition leader Mir Hossein Mousavi at a separate rally in central Tehran. Mousavi and his wife attended one of the rallies, it said.
Another opposition site, Norooz, said 30 people were arrested in one Tehran square. A third, Jaras, said security forces attacked another opposition leader, Mehdi Karoubi, and former President Mohammad Khatami. It said the windows of Karoubi's car were smashed but he was not seriously hurt.
Jaras said at least 100 mainly young protesters were detained in the northeastern city of Mashhad, and there were some "limited" clashes with security forces. It said more than 20 people were detained in the southern city of Shiraz, as anti-riot police sought to prevent protesters from gathering.
However, there were no reports of the kind of violence that erupted in late December, when eight people were killed in clashes between security forces and opposition supporters.
Neither side has shown much appetite for compromise in the eight months since the presidential vote, which the opposition says was rigged to secure Ahmadinejad's re-election. The authorities insist it was fair.
Since June, thousands of people protesting against the conduct of the vote have been arrested. Most have since been freed, though more than 80 people have been jailed for up to 15 years, including several senior former officials.
In January, Iran hanged two people sentenced to death in post-vote trials. At least nine others are appealing such sentences.
The country faces growing Western calls for a new round of targeted United Nations sanctions against it after Ahmadinejad this week ordered a start to production of higher-grade uranium.
Iran says it moved to produce the 20 percent enriched uranium for a Tehran research reactor making medical isotopes out of frustration at failure to reach agreement on a uranium exchange with world powers.
"By God's grace ... it was reported that the first consignment of 20 percent enriched uranium was produced and was put at the disposal of the scientists," Ahmadinejad said. "In the near future we will treble its production." Iran had previously purified the fuel to just 3.5 percent, the level required for a nuclear power plant.
Western experts say the jump to 20 percent is a major technical leap toward enriching uranium to the 90 percent-plus that would be needed for a nuclear bomb.
The West accuses Iran of covertly trying to build nuclear bombs. Iran, the world's fifth-largest crude oil exporter, says its nuclear facilities are part of a peaceful energy program and it would retaliate for any attack on them.
Referring to comments by US President Barack Obama this week that the international community was moving "fairly quickly" toward imposing broader sanctions on Iran, Parliament Speaker Ali Larijani said in the city of Qom: "If Obama, who found the courage to threaten Iran yesterday, makes this maneuver again, Iran's answer will be speeding up its nuclear technology."
British Prime Minister Gordon Brown told BBC television: "I believe the mood around the world is now increasingly one where, patience not being inexhaustible, people are turning to look at the specific sanctions we can plan on Iran."
