Ayatollah Ali Khamenei, in a speech broadcast by state television, also said the opposition had encouraged Iran's enemies to undermine the Islamic system.
Referring to a disputed June election which the opposition says was rigged in favour of hardline President Mahmoud Ahmadinejad, Khamenei said: "The election is over. It was legal and they could not demonstrate their claim."
Earlier, the opposition expressed concern that the authorities were preparing to step up action against it after official media said pro-reform students had torn up a picture of the Islamic revolution's father, Ayatollah Ruhollah Khomeini, during a rally last Monday.
Khamenei said the opposition rallies were illegal and he urged authorities to identify "those behind the insult to imam Khomeini".
Some reformist websites have suggested opposition leader Mirhossein Mousavi may be arrested, six months after his election defeat by Ahmadinjad plunged Iran into turmoil.
Hardliners have in the past called for Mousavi to be prosecuted for fomenting street unrest.
Khamenei said the opposition rallies were illegal and he urged authorities to identify "those behind the insult to imam Khomeini".
NO INSULTS TOLERATED
State television has broadcast footage of what it said were opposition supporters tearing up and trampling on a picture of Khomeini during the anti-government demonstrations on Dec.7.
A student rally on that day turned violent when reformist students clashed with security forces.
Khomeini, who led the 1979 overthrow of the U.S.-backed Shah, remains widely revered in Iran. He died in 1989 and was succeeded by Khamenei as supreme leader, Iran's highest authority under its government system of clerical rule.
The elite Revolutionary Guards said in a statement: ""We, as followers of Imam Khomeini, will not tolerate any shortcoming in identifying, trying and punishing those behind the insult and those who carried it out,"
Mousavi, who advocated a return to Khomeini's fundamental values during his election campaign, has been quoted as condemning the incident relating to the picture. But hardliners still clearly blamed his supporters.
Clerics from theology schools and other leadership loyalists staged pro-government rallies in cities across Iran on Saturday, chanting "Death to America" and "Death to opponents of the Supreme Leader," official media reported.
More such rallies were scheduled for Sunday, including at the Imam Khomeini shrine outside Tehran and at universities.
Any detention of Mousavi, may provoke new opposition demonstrations.
The election plunged Iran into its deepest internal crisis since the revolution three decades ago and exposed deepening divisions within the establishment.
Thousands of Mousavi supporters were detained after the vote, including senior reformers. Most have been freed but about 80 people have received jail terms of up to 15 years and five have been sentenced to death over the post-vote unrest.
Analysts say the internal crisis has further clouded prospects for any resolution of a long-running row with the West over Tehran's nuclear programme, which the United States suspects is aimed at making bombs. Tehran denies this.
(Editing by Angus MacSwan)
