Tehran, Iran (CNN) -- Several people were killed and more than 300 were arrested in anti-government protests in Tehran Sunday, Iran's Deputy Police Chief Ahmad Reza Radan said on state television station IRINN.

The toll was the result of clashes that broke out between demonstrators and security forces as large crowds gathered for Ashura, a major religious observance.

Five people were reported killed in the fighting, Iranian state-run Press TV said late Sunday. A French government statement put the number of fatalities at eight. With tight restrictions on international media, CNN could not independently verify the casualties.

Without giving an exact number of casualties, Radan said those killed included one person who fell off a bridge and two others who were killed in a car accident during the protests.

One of the victims was killed by a bullet, Radan said. But "considering the fact that the police did not use firearms, this incident is extremely suspicious, and is being investigated," he said.

The Web site of opposition leader Mir Hossein Mousavi reported that Mousavi's nephew, Seyed Ali Mousavi, was killed in the demonstrations around noon local time Sunday by a gunshot to the heart.

Press TV, meanwhile, late Sunday quoted unnamed police officials as identifying one of the dead as "Seyyed Ali Mousavi."

Press TV's report did not mention any relationship between that victim and opposition leader Mousavi, nor did its report include any mention of the elder Mousavi.

Tehran Police Chief Azizollah Rajabzadeh denied any protesters were killed by security forces.

Are you in Iran? Share your photos and video and tell us what's going on.

Police did not fire any shots in Tehran, "and security forces were not in possession of firearms," Rajabzadeh told the semi-official news agency ISNA.

Since the disputed presidential elections in June, protesters have turned public gatherings into rallies against President Mahmoud Ahmadinejad, who was declared the overwhelming winner of the race.

Police, wary of the potential that Ashura gatherings could present, were out in full force Sunday to quell disruptions but did not stop demonstrators holding widespread protests.

Near Imam Hussein Square in central Tehran, security forces used tear gas to disperse demonstrators and blocked roads to prevent more from arriving, a witness said.

Protesters seized a motorcycle belonging to a security force member and set it on fire.

Elsewhere in the city, witnesses reported seeing protesters being beaten with batons. Demonstrators chanted "death to the dictator" and some ripped down a picture of Iran's Supreme Leader Ayatollah Khamenei.

Police helicopters hovered above city squares while small trucks brought in more riot police in parts where clashes were fierce.

Protesters played cat-and-mouse with security forces -- gathering, then scrambling and gathering elsewhere.

U.S. National Security Council Spokesman Mike Hammer said the United States condemns the "violent and unjust suppression of civilians in Iran seeking to exercise their universal rights."

"Governing through fear and violence is never just, and as President Obama said in Oslo -- it is telling when governments fear the aspirations of their own people more than the power of any other nation," Hammer said in a statement.

The French Foreign Ministry issued a statement Sunday expressing "great anxiety" following the violent clashes.

The statement said at least eight people were killed and several were wounded in the clashes.

France condemns the arbitrary arrests and the "acts of violence committed against demonstrators who came to defend their right to freedom of speech and their aspiration to democracy. Facing the persistence of popular movements and the worsening of the repression, France is calling for a political solution in Iran," the ministry's statement said.

The unrest Sunday followed daylong clashes between the two sides in the streets of Tehran on Saturday.

On Saturday evening, a pro-government mob barged into a mosque where former president and reformist leader Mohammad Khatami was speaking.

The dozens-strong group forced Khatami to end his remarks abruptly when it interrupted the gathering at Jamaran mosque.

Earlier Saturday, scores of security forces on motorcycles charged protesters on sidewalks whenever they started chanting anti-government slogans, witnesses said.

Sunday marks Ashura, the observance of the death of Imam Hussein, grandson of Prophet Muhammad.

Hussein, who was killed in battle in Karbala in 680 A.D., is regarded as a martyr. The battle that led to his death is one of the events that helped create the schism between Sunnis and Shiites, the two main Muslim religious movements.

Iran is predominantly Shiite.

During Sunday's protests, some demonstrators compared Khamenei to Yazid, the caliph who killed Hussein.

Religious mourning during Ashura is characterized by people chanting, beating their breasts in penance, cutting themselves with daggers or swords and whipping themselves in synchronized moves.

Sunday also is a week to the day since the death of Grand Ayatollah Hussein Ali Montazeri, a key figure in the 1979 Iranian revolution. Montazeri, who went on to become one of the government's most vocal critics, died December 20.

The seventh day after a death is a traditional time for mourning in Islam.

CNN's Reza Sayah contributed to this report.