"This is a great victory at a time when the ... propaganda facilities outside Iran and sometimes inside Iran were totally mobilised against our people."
Ahmadinejad praised the country's youth, but made no direct mention of the protests.
Al Jazeera's Teymoor Nabili, reporting from Tehran, said major streets in the north of the city had come to a standstill.
"Coming up the street there were running battles happening between riot police and students and there were refuse bins alight in the middle of the road," he said.
"I saw riot police hitting students with sticks. I saw students - or young people - throwing stones at the riot police, trying to knock them off their motorcycles.
"But you didn't get a sense that there was any kind of organised movement in this."
Mohsen Khancharli, Tehran's deputy police chief, warned that his officers would "strongly confront" any gathering or rally held without permission.
"Police are not confronting people but only those who are disturbing public order or who make damage to public places," he told Iran's official IRNA news agency.
Fearing the protests might spread, authorities blocked access to some news websites and Facebook, the social networking site.
"Text messaging has been closed all day and now its very difficult to even get a mobile telephone line," our correspondent said.
Ahmadinejad was declared the winner by a wide margin in Friday's election, with figures from the interior ministry showing he had taken 62.63 per cent of the vote, while Mousavi garnered only 33.75 per cent.
The scale of Ahmadinejad's triumph upset widespread expectations that Mousavi might win the race.
But supporters of Ahmadinejad also took to the street following the announcement of his victory, waving Iranian flags and honking car horns in celebration of his winning a second, four-year term.
Mehran Kamrava, director of the centre for international and regional studies at Georgetown University's campus in Qatar, said that protests in northern Tehran were not necessarily an indication of a rigged ballot.
"The Western media has been talking to people in north Tehran, who tend to vote overwhelmingly against Ahmadinejad," he told Al Jazeera.
"But let's not forget that many of the urban Iranians have priorities and proclivities that are not necessarily reflected in other areas of the main cities, and those people could easily have voted for Ahmadinejad.
"Iranian politics have proved themselves to be notoriously unpredictable and this could be one of those instances of unpredictability."
Mousavi said that members of his election headquarters had been beaten "with batons, wooden sticks and electrical rods".
He also appealed directly to Ayatollah Ali Khameini, Iran's supreme leader, to intervene and stop what he said were violations of the law.
|Several people were injured in the protests, sparked by the election results [AFP]
But Khameini appeared unlikely to intervene, calling on defeated candidates and their supporters to avoid "provocative behaviour".
"The chosen and respected president is the president of all the Iranian nation and everyone, including yesterday's competitors, must unanimously support and help him," he said in a statement read on state television.
Earlier, Mousavi urged his supporters to avoid violence while acknowledging their right to be deeply hurt by the alleged violations in the election.
"I firmly call on you not to subject any individual or groups to hurt. Do not lose your calm and restraint," Mousavi said in a statement posted on his campaign website.
"Everybody should draw a line between themselves and any violent behaviour."
Iran's elections have seen allegations of vote rigging in the past.
During the 2005 election, when Ahmadinejad won the presidency, there were some allegations of fraud, but the claims were never investigated.
Iran does not allow international election monitors.