The opposition Jaras website also said security forces attacked a building housing an Iranian news agency, ISNA, where it said some demonstrators had sought shelter during the clashes.
A witness said at least two people were injured when police chased after protesters into the downtown building.
They fractured the skull of one ISNA person and badly beat up another employee, the witness said. ISNA's news service appeared to be working normally, and its reports made no mention of security forces breaking into its building.
The outbreak of clashes during a two-day major Shi'ite Muslim religious ritual would underline escalating tension in the Islamic Republic, six months after a disputed election plunged the major oil producer into turmoil.
Despite scores of arrests and security crackdowns, opposition protests have repeatedly flared since the June poll, which the opposition says was rigged to secure hardline President Mahmoud Ahmadinejad's re-election.
Well-equipped security forces are clashing violently with backers of the opposition in many parts of downtown Tehran, Jaras said. Opposition supporters sought shelter inside the building of students news agency ISNA to protect themselves ... Police attacked ISNA's building.
It later added: Riot police are shooting into the air in Enqelab square to disperse demonstrators who chant anti-government slogans.
The official IRNA news agency blamed foreign media for exaggerating the unsuccessful gathering of rioters and for trying to encourage people to take to the streets. It said the rioters numbered only 150 people, adding they wanted to disrupt the mourning ceremonies but that police dispersed them.The Jaras reports could not be independently verified as foreign media are banned from covering post-election protests. In another part of Tehran, police stopped a Reuters photographer to check whether he had taken pictures of protests.
Police had warned the pro-reform opposition against staging any new rallies during Tasoua and Ashura on Dec 26-27, when Shi'ite Muslims mark the 7th century martyrdom of a grandson of the Prophet Mohammad.
Indicating possible further unrest, the opposition Green Movement urged people to gather in the same Tehran area also on Sunday morning, according to mobile phone text messages.
The opposition Norooz website said families of senior reformist figures detained after the June election, which sparked huge opposition protests, would gather on Sunday to call for their release.
Ahmadinejad's re-election kindled the biggest unrest in the Islamic state's 30-year history and split the political and clerical establishment.
MONTAZERI MOURNING BAN
Authorities deny the opposition's vote rigging charges and have portrayed the huge protests that erupted after the poll as a foreign-backed bid to topple the Islamic establishment, accusing leading reformers of fomenting post-election violence.
Thousands of people were arrested after the poll. Most of them have since been freed, but more than 80 have received jail sentences of up to 15 years in connection with protests and violence after the vote, the judiciary says.
Ahmadinejad said Iran's foreign foes could not harm the Islamic state from inside the country, Fars News Agency said.They had planned a very complicated and wideranging scenario ... but they don't know that a nation which is ready to sacrifice its life for its religious figures will destroy all their satanic attempts, he said.
Iran's internal unrest has complicated a long-running international dispute over its nuclear programme, which the West believes may have military ends, not just civilian purposes.
Saturday's reported clashes come just days before an end-of-year deadline set by world powers for Iran to agree a U.N.-drafted deal to ship most of its low-enriched uranium abroad in exchange for fuel for a Tehran research reactor.
Tension rose again in Iran after the death a week ago of leading dissident cleric Grand Ayatollah Hossein Ali Montazeri at the age of 87 in the holy Shi'ite city of Qom.
Montazeri, an architect of the 1979 Islamic revolution, was once named to succeed late revolutionary leader Ayatollah Ruhollah Khomeini as supreme leader. He fell from grace after criticising the mass execution of prisoners in the late 1980s.
A spiritual patron of the pro-Mousavi movement, he was a fierce critic of the hardline clerical establishment who denounced Ahmadinejad's re-election as fraudulent.
(Editing by Dominic Evans)