"These work like an army. This is our army against their military force."
Mousavi supporters believe he was the real winner of last year's disputed vote, which went in favour of Mahmoud Ahmadinejad, the incumbent president.
Troops used deadly forceto quell the large-scale street protests that erupted after the result was announced.
In the lead-up to Saturday's anniversary, authorities had vowed to crack down on any renewed protests.
Morteza Tamadoon, the governor of Tehran, had said that "any illegal move to disrupt public order and trouble people will not be tolerated and will be dealt with".
Still, witnesses reported sporadic but minor clashes in the Iranian capital.
At Sharif University of Technology in Tehran, students scuffled with government supporters and plainclothes paramilitary personnel on campus, according to Mousavi's website.
Security forces arrested a political ally of Mousavi, Davoud Roshani, and Reza Shahabi, a labour union activist, Mousavi's website reported.
Several dozen opposition activists also took part in a protest rally in the UK's capital, London.
Ahmadinejad's re-election divided Iran's political elite, and the government's subsequent crackdown on protesters drew international condemnation.
The authorities led by Ayatollah Ali Khamenei, the supreme leader, blamed the unrest on Western powers, accusing them of masterminding the protests in a bid to topple the Islamic regime.
But Mousavi, who is a former prime minister, and Mehdi Karroub, an ex-parliament speaker, who were close to Ayatollah Ruhollah Khomeini, father of Iran's Islamic revolution, have dismissed such allegations.
In the run-up to the anniversary, Barack Obama, the US president, urged the world to support the Iranian peoplein their fight for "freedom".
The US has had no diplomatic ties with Iran for three decades.
Obama made the statement on Thursday after Hillary Clinton, the US secretary of state, called the opposition decision to cancel anti-government protests "regrettable".
"The courage of the Iranian people stands as an example to us and it challenges us to continue our efforts to bend the arch of history in the direction of justice," he said.