Riot police and members of Basij, a pro-government armed volunteer force, were deployed heavily in Tehran.
Witnesses said 1,000 protesters gathered at the Haft-e Tir Square despite the guards' warning.
One witness said he saw Basij members attack a group of protesters, dragging them out of a nearby house to which they had fled, the Reuters news agency reported.
In New York on Monday, Ban Ki-moon, the UN secretary-general, called for an immediate stop to the use of force against civilians and said Iranian authorities should respect civil rights in dealing with the protests.
In a statement Ban called on Iran's government "to respect fundamental civil and political rights, especially the freedom of expression, freedom of assembly and freedom of information".
Earlier in a warning to protesters Iran's Revolutionary Guard said they would not hesitate to confront "illegal" rallies organised by supporters of Mir Hossein Mousavi, the moderate politician who is contesting the re-election of Mahmoud Ahmadinejad.
"At the current sensitive situation ... the guards will firmly confront, in a revolutionary way, rioters and those who violate the law," the Guards' statement said.
The Iranian government has also cracked down on independent media reporting on the protests, and imposed severe restrictions on foreign journalists.
The Iranian capital has seen unrest and street protests since results of the vote were announced on July 13.
Over the weekend, clashes between police and anti-government protesters left at least 12 people dead and more than 100 wounded - raising the death toll to 19 since the unrest began.
Iranian state radio reported that more than 450 people had been arrested during Saturday's rallies, mostly around Tehran's Azadi Square.
Forty police officers were also wounded, and 34 government buildings damaged, the Fars news agency reported.
Despite the deaths, arrests and an earlier warning from Ayatollah Ali Khamenei, Iran's supreme leader, the demonstrators appear to be undeterred.
Alireza Zaker-Esfahani, an adviser to Ahmadinejad, accused Mousavi of not trying to calm his supporters.
"The weakness is in Mir Hossein Mousavi's political behaviour. ... He is currently issuing statements inviting his supporters to take to the streets. That will not solve any problem," he told Al Jazeera on Monday.
"Rallies will ultimately contribute to abuse, setting buses on fire, bloodshed and constant insecurity for the people."
Earlier, Iran's Guardian Council, the country's highest legislative body, admitted some irregularities occurred during the election.
Abbas-Ali Kadkhodaei, the council's spokesman, told state-funded broadcaster IRIB on Monday that up to three million votes were under scrutiny, after it was found that the number of votes exceeded the number of eligible voters in 50 cities.
However, he said it was a normal discrepancy because people are allowed to travel to other areas to vote, and that it was "yet to be determined whether the amount is decisive in the election results".
Ahmadinejad won the election by a wide margin, with 63 per cent of the vote, according to figures from Iran's interior ministry.
The ministry said Mousavi received only 34 per cent of the vote.
He and his supporters allege voter fraud and have called for an annulment of the result.
"Lies and fraud"
Ghanbar Naderi, an Iranian journalist and Ahmadinejad supporter, told Al Jazeera that the Mousavi camp is underestimating the support Ahmadinejad received in areas outside the capital.
"They are ignoring the fact that there are so many poor people across the country who really favour Ahmadinejad," he said on Monday.
|User-supplied images are the chief source of information from Iran for the world's media
"Ahmadinejad has directed his development programmes across provinces in deprived areas, in remote areas, and people saw the results of his promises - he delivered on his promises. That is why they voted for him."
In a statement published on the website of his newspaper Kalameh, Mousavi said that Iranians had the right to protest against "lies and fraud", but also urged them to show restraint as they take to the streets.
"The revolution is your legacy. To protest against lies and fraud is your right. Be hopeful that you will get your right and do not allow others who want to provoke your anger ... to prevail," he said.
Atoosa, a Mousavi supporter, described Mousavi's call to show restraint as a "smart move".
"As we have seen, the crackdown is very hard on people and people are dying everyday," she told Al Jazeera by phone from Tehran on Monday.
"The only way to protest now is to use different methods."
Al Jazeera is not responsible for the content of external websites.