Mir Hossein Mousavi, who was Ahmadinejad's main rival in the election, suggested in a statement on his website that a protest rally would be held.
"The 13th of Aban is ... a rendezvous so we can remember anew that among us it is the people who are the leaders," he said, referring to the Iranian date for the capture of the US embassy.
Our correspondent in Tehran said: "The phone lines have been cut and we cannot access email from our offices, but what we are hearing and seeing from pictures being fed from the streets of Tehran are thousands of anti-government protesters who have been chanting pro-Mir Hossein Mousavi slogans and "death to the dictator" as well.
"We also understand that Mehdi Karroubi, one of the presidential candidates, on his way to [Haft-e-Tir] square was attacked.
"We understand he is OK, but two of his guards have been injured after attacks by pro-government supporters."
The opposition protesters are expected to head for the Russian embassy later on Wednesday.
"We have heard for 30 years what the Iranian government is against; the question, now, is what kind of future it is for"
"Many people, rightly or wrongly, thought China and Russia were behind what happened with President Ahmadinejad, what happened in the election," Baqer Moin, an Iranian author and journalist, said.
"It has been seen in various demonstrations that while the officials have been shouting anti-American slogans, they [the opposition] have been responding with anti-Russian slogans," he told Al Jazeera from London.
Outside the now-closed US embassy, many more Iranians gathered chanting "Death to America", "Death to England" and "Death to Israel".
Iranian student activists entered the US embassy on November 4, 1979, taking 52 Americans hostage in response to Washington's refusal to handover Mohammad Reza Pahlavi, the shah deposed by the Islamic Revolution.
The hostages were held for 444 days before their release was secured.
Grand Ayatollah Hossein Ali Montazeri, a senior Iranian religious leader, said on Wednesday that the capture of the US embassy was a mistake.
"The occupation of the American embassy at the start had the support of Iranian revolutionaries and the late Imam Khomeini [Iran's former supreme leader] and I supported it too," he said in a statement posted on his website.
|The US staff at the embassy were held for
444 days after students broke in [File: EPA]
"But considering the negative repercussions and the high sensitivity which was created among the American people and which still exists, it was not the right thing to do."
Montazeri was one of the senior leaders of the Iranian revolution but disagreed with Khomeini later over government policies that he claimed infringed freedom and denied people's rights.
Barack Obama, the US president, chose the anniversary to appeal to Tehran to "choose" its future path.
"It is time for the Iranian government to decide whether it wants to focus on the past, or whether it will make the choices that will open the door to greater opportunity, prosperity, and justice for its people," he said in the statement .
"We have heard for 30 years what the Iranian government is against; the question, now, is what kind of future it is for."
'Hiding a dagger'
Tehran and Washington are locked in dispute over Iran's nuclear programme, which the US and its allies fear is a cover for an atomic weapons programme. Iran says it is enriching uranium only to meet its civilian energy needs.
Speaking before the anniversary, Ayatollah Ali Khamenei, Iran's supreme leader, criticised the US for ongoing negotiations over a nuclear fuel deal that would see it hand over its supply of low-enriched uranium to outside powers.
"Every time they have a smile on their face, they are hiding a dagger behind their back," he said.
"They are telling us to negotiate, but alongside the negotiation there is a threat... We do not want any negotiation, the result of which is pre-determined by the United States."