The interior ministry said the planned march against the re-election of President Mahmoud Ahmadinejad had been planned by "sedition elements".
Mr Mousavi, a moderate, called for the results to be annulled, alleging fraud.
Mr Ahmadinejad says the poll was fair. Tens of thousands rallied in Tehran on Sunday to celebrate his victory.
Responding to the opposition move, the interior ministry: "Some seditious elements had planned to hold a rally."
It added: "Any disrupter of public security would be dealt with according to the law."
'Death to the dictator'
There were clashes between the police and anti-Ahmadinejad protesters in several parts of the city for a second day on Sunday.
Police hit protesters with batons and charged them on motorbikes.
Mousavi supporters cried "death to the dictator" into the evening. Scores of people are reported to have been arrested.
There have been reports of tear gas being fired and rooms being searched at Tehran University.
The BBC's Jon Leyne in Tehran says the rapidly spreading protests are a challenge not just to the election result, not just to President Ahmadinejad, but to the supreme leader, Ayatollah Ali Khamenei himself.
That means it is, he says, a challenge to the whole basis of the Islamic Republic.
Mr Ahmadinejad dismissed the unrest as "passions after a soccer match".
International concern
Mr Mousavi's website carried a statement saying he had formally called on Iran's Guardian Council, which must certify the counting, to annul the election.
He added: "I urge you, Iranian nation, to continue your nationwide protests in a peaceful and legal way."
A supporter of Mr Mousavi, Shahab Tabatabaei, told the Associated Press news agency the candidate had met Ayatollah Khamenei to press his call.
But the BBC's John Simpson in Tehran says the call is almost certain to fail.
The Reuters news agency said Mr Mousavi's supporters were planning a rally on Monday afternoon but it was unclear whether the authorities would allow it.
One of the country's leading dissidents, Ibrahim Yazdi, told the BBC there had been clear signs of fraud in the poll, with detailed results being withheld.
More foreign powers are also expressing concern about the election.
In an interview on US television, Mr Biden said: "It sure looks like the way they're suppressing speech, the way they're suppressing crowds, the way in which people are being treated, that there's some real doubt."
German Foreign Minister Frank-Walter Steinmeier said he had summoned the Iranian ambassador to explain the election.
"There are a lot of reports about electoral fraud," he said.
French Foreign Minister Bernard Kouchner said: "I am sorry that instead of openness there has been a somewhat brutal reaction."
But Mr Ahmadinejad was congratulated by the presidents of Iraq, Afghanistan and Venezuela.
At his rally on Sunday, Mr Ahmadinejad denied any vote-fixing, saying the result was "very accurate".
Crowds thronged the main thoroughfare, Vali Asr street, waving Iranian flags and chanting in jubilation.
He told the rally that elections in the Islamic republic had never been healthier and that the people alone had decided the outcome.
"Some people want democracy only for their own sake," he said, referring to his critics both inside and outside of Iran.
"Some want elections, freedom, a sound election. They recognise it only as long as the result favours them."
He said Iranians were united, but with 40 million people taking part in the election it was natural for some to be disappointed.
Unrest flared after a high turnout in Friday's election - estimated at 85% - led Mr Mousavi's supporters to expect a close result.
But official results gave Mr Ahmadinejad a landslide victory. His final share of the vote was almost 63%.
The result was quickly endorsed by Ayatollah Khamenei.
