In one instance, a group of Iranian protesters attacked Mohammad Khatami, a reformist former president, while he was marching with opposition supporters in Tehran, a reformist website reported.
The Parlemennews site cited witnesses as saying the attackers pushed Khatami to the ground, but opposition activists quickly repelled the attackers.
"During the scuffle, his turban fell off and they wanted to beat him. But supporters resisted them and the riot police promptly intervened," it reported.
Mohammad Reza Khatami, Khatami's brother, said the former president, a key supporter of Iranian opposition groups, was "not hurt" in the attack, the AFP news agency reported.
The opposition had called for mass protests to coincide with the government-sponsored demonstration marking the day.
But Iran's Revolutionary Guard warned on Thursday that it would crack down to halt any anti-government rallies.
"This nation's brave children who are in the security bodies and the police, or in the Revolutionary Guards or the Basij (are ready) to confront firmly any deviation, and anti-revolutionary ... moves," the Guards said in a statement published by the state news agency, Irna.
Ayatollah Ali Khamenei, Iran's supreme leader, has also warned the opposition against using the al-Quds Day rally to launch street protests.
"Be watchful so some who want to spread division do not succeed. No division should be created," he said recently.
Ayatollah Ruhollah Khomeini, the late founder of Iran's 1979 Islamic revolution, declared the last Friday of the Muslim holy month of Ramadan as al-Quds Day, calling for international rallies in support of Palestinians and against Israel.
Mahmoud Ahmadinejad, Iran's president, who is accused by opposition groups of rigging his re-election in June, marked the solidarity day with an address at a rally at Tehran University.
He used the address to denounce Israel, saying the Holocaust was a "false pretext" used to create the state and that confronting the "Zionist regime" is a national and religious duty.
Similar comments made by Ahmadinejad in 2005 sparked international criticism.
Al Jazeera's Alireza Ronaghi, reporting from Tehran, said security forces were out in force, attempting to keep opposition demonstrators away from the university.
Ronaghi said Ahmadinejad's address marked a chance for the Iranian leader to show that his positions on Israel and the West remain unchanged.
"It's a very important opportunity for President Ahmadinejad to emphasise once again that his anti-Israeli and anti-Western stance hasn't changed a bit by all that has happened after the election," he said.
"There have been accusations that Ahmadinejad is going to solve the government's problems with the West. One of the major sticking points would be Iran's stance against Israel.
"So it's very important for him to emphasise that he's not going to change that any time soon."
Ahmadinejad's main rivals, Mir Hossein Mousavi and Mehdi Karroubi, the defeated presidential candidates, had also been expected to take part in the main al-Quds Day march.
But the official Irna news agency said he was prevented from taking part in the rally after an angry crowd attacked his car.
Mousavi and Karroubi had led mass protests in the wake of the elections, sparking a major crackdown by police and the detention of hundreds of people.
"All of us regret the fact that some people were killed"
Mahmoud Ahmadinejad, Iran's president
The opposition says at least 69 people were killed in the crackdown, including some who died from torture in prison.
The June election returned Ahmadinejad to power, but the opposition has disputed the poll, saying it was rigged.
Ahmadinejad told US television network NBC News that he regretted the deaths of protesters during the demonstrations.
"All of us regret the fact that some people were killed," he said in excerpts of an interview to be aired on Sunday.
But he said he did not "see any problems" with the credibility of the June 12 election.
More than 100 prominent opposition supporters are now on trial on accusations of plotting to use the anti-election protests to overthrow Iran's clerical leadership.