Al Jazeera's Alireza Ronaghi, reporting from Tehran, said the police had prevented Mir Hosseini Mousavi, one of the defeated reformist candidates in the disputed June 12 presidential election, from standing at the Behesht-e Zahra cemetery longer than he was going to be there to recite the Koran.
He said they had led him back to his car and forced him to leave.
Witnesses said Mousavi had managed to get out of his car and walk up to the grave of Neda, who was killed on June 20.
Neda, a 26-year-old music student, was shot as protesters clashed with riot police and members of the pro-government Basij militia in Tehran.
At least 20 people are believed to have been killed and several thousands arrested in the crack down following the re-election of Mahmoud Ahmadinejad, the Iranian president, in the contested vote.
Mehdi Karroubi, another reformist candidate, also attended the graveside service.
Several people accused of rioting during the post-election protests are to go on trial from Saturday on a range of charges including attacks on government and military offices, arson, vandalism and contacts with "enemies", including the People's Mujahideen, a banned opposition group.
"We have pictures showing them committing these crimes," Saeed Mortazavi, the Tehran prosecutor, said on Wednesday.
However, there was also an apparent acknowledgement of abuse by members of the security forces as they targeted protesters, political activists and journalists in the aftermath of the election.
"Some officers went to extremes in these incidents and they inflicted damage on people while chasing the rioters," Esmail Ahmadi Moghaddam, Iran's police chief was quoted as saying.
"Nothing should make our forces break the law."
The unrest following the presidential poll has also exposed the divisions between the conservatives and reformists in the country's ruling elite.
Rasool Montajebnia, Karroubi's deputy, has suggested that Mousavi, a former prime minister, Karroubi and Mohammad Khatami, a former president, form a joint council to advance the opposition movement.
"If they individually carry out actions, it cannot become a comprehensive movement and address people's demands," he was quoted as saying by Karroubi's Etemad Melli newspaper.
"There is no way but to establish a council of reform ... around the axis of Khatami, Karroubi and Mousavi."
Karim Sadjadpour, an Iranian expert at the Carnegie Endowment for International Peace, told Al Jazeera that the tense situation in Iran was no longer about the elections.
"It's about people's sense of dignity, their sense of justice and people's hopes for the future of Iran.
"Today, I think people feel the sense of outrage and injustice transcends socioeconomic class, age, geography and gender and what we have seen is that there are incredible fissures even at the levels of the political elite and the security forces as well," he said.
Ahmadinejad is due to be sworn in as president next week, but his standing has been weakened after Ayatollah Ali Khamenei, Iran's supreme leader, ordered him to dismiss his choice for first vice-president.
Sadjadpour said: "Ahmadinejad's future is incredibly tenuous and sometimes he is described as a skilled political but nothing could be further from the truth. He's actually a very poor politician in the sense that he gratuitously alienates even the people within his own party.
"If his government is allowed to stand, it's not going represent not only a very narrow swath of Iranian society, but even a very narrow swath of the Iranian political elite and what we've seen over the last week or two is that Ahmadinejad has even managed to alienate his chief patron, supreme leader Ayotallah Khameini."