Tehran police said five people were "suspiciously killed". "Specialists are trying to identify the suspect perpetrators of this incident," said a statement carried by the official IRNA news agency.
Police arrested more than 300 people, deputy police chief Ahmad Reza Radan told state television.
He confirmed four people had died but said one had fallen off a bridge and two had died in car accidents. The fourth had died of bullet wounds, but he denied that the security forces were responsible.
"As the police were not using firearms this is suspicious and it is being investigated," he said.
Witnesses said police used batons and tear gas in the crackdown, which followed stern warnings by the authorities that they would crush attempts to use Ashura processions as a launchpad for protests.
When this failed to disperse the crowds, they opened fire, websites said.
Parlemannews said Seyed Ali Mousavi, the 35-year-old nephew of Mousavi, was shot near his heart during clashes at Enghelab square "and was martyred after he was taken to Ebnesina hospital."
Mousavi and other family members were at the hospital along with some political figures, said the website, which is run by the parliament's minority reformist faction which backs the opposition.
Police had earlier denied that anyone had died in the clashes, which witnesses said came after tens of thousands of opposition supporters took to the streets for a second straight day to use the Ashura rituals to protest.
The authorities' response again drew international criticism.
The White House strongly condemned "violent and unjust suppression" of civilians.
The blunt statement contrasted with careful initial responses by Washington after election protests in June and came as the showdown with Iran over its controversial nuclear programme reached a critical point.
The French foreign ministry criticised the police action against "simple protestors" and called for a political solution.
Witnesses said that enraged protesters fought back against the security forces, pelting them with stones and chanting: "We fight and we die to get back Iran."
They beat up several policemen and set their pick-up truck on fire, witnesses said, adding that the policemen ran away with blood streaming down their faces.
Many protesters, including women, were chanting "Death to the dictator" and "It is the bloody month and the basij will fall," referring to the Islamist militia which plays a key role in suppressing protests.
They also chanted "Ya Hossein, Mir Hossein" in support of Mousavi.
AFP was not able to verify the various reports as the foreign media is banned from covering opposition demonstrations.
Syrian journalist, Reza al-Basha, 27, an Iran-based correspondent for Dubai TV, was feared to be among those arrested, a colleague told AFP.
Rahesabz also reported heavy clashes between protesters and security forces in Isfahan and Najafabad -- the home town of late dissident cleric Grand Ayatollah Hossein Ali Montazeri -- in the northern city of Babol and in the southern city of Shiraz.
It added that clashes broke out in Iran's second city Mashhad and the central city of Arak and cited "unconfirmed reports" of casualties in Tabriz, Iran's main northwestern city.
Opponents of Ahmadinejad's June 12 re-election have used a series of government-backed public events to mount protests, many of which have ended in clashes with police.
The last known deaths during street protests in Tehran were on June 20. The opposition says that at least 72 people were killed in June's protests while the authorities put the figure at 36, including members of the basij.
Three protesters also died in custody after being beaten.