While the streets of Tehran were largely calm, the BBC's Jon Leyne, in the city, reports that clashes broke out by the office of Irna, Iran's official news agency, and also in one suburb.
There were also new reports of a clampdown on independent media.
The offices of the Saudi-funded Arabic TV station al-Arabiya were shut down for "unknown reasons", the channel said.
Mobile phone service was restored but there were reports that text messaging remained restricted and curbs continued on access to popular internet sites, including the BBC.
Mr Ahmadinejad is expected to attend a huge victory rally later on Sunday.
Jon Leyne Reporting from Tehran
President Mahmoud Ahmadinejad has always seen himself as more than just a politician. Sometimes he speaks, and is treated, more like a seer prophesying the death of capitalism and liberal democracy. With this victory, however secured, he will feel emboldened in this global vision.
At home, many Iranians will fear a clampdown on society and cultural life. Mr Ahmadinejad knows that many even within the political establishment oppose him, which might increase his tendency towards authoritarianism. All those young people who were out campaigning against him so recently will be nervous about their future, and even more disillusioned with the Islamic Republic.
Then there is foreign policy and the nuclear issue. How can US President Barack Obama open negotiations with a president whose legitimacy and human rights record is even deeper under question? It is a political earthquake that will shake Iran, and could shake the world.
Details of latest arrests remained sketchy, but reports said those detained were members of pro-reformist political parties which had backed Mr Mousavi during the election campaign.
The reformists - said to include Mohammad Reza Khatami, brother of former President Mohammad Khatami, a former government spokesman and a former deputy speaker of parliament - were reported to have been taken from their homes by security forces overnight.
Iran's state news agency, Irna, said those arrested were involved in orchestrating Saturday's protests in Tehran.
Mr Mousavi's whereabouts are unknown but he is thought to remain free.
Angry crowds took to the streets to protest against President Mahmoud Ahmadinejad's re-election, in spite of Mr Mousavi's post-election call to avoid violence.
He has refused to accept the election result, calling it a "dangerous charade" and alleging wide-scale irregularities
The BBC's foreign affairs editor John Simpson, in Tehran, says that while the protests appeared to be an upsurge of anger amongst ordinary people and did not appear to be arranged, it is an instinctive reaction by the authorities to see a hidden hand.
Senior Iranian political figures have offered their backing to Mr Ahmadinejad, among them parliamentary Speaker Ali Larijani and the head of the judiciary.
President Ahmadinejad: 'The election process in Iran is a very accurate one'
One of his defeated rivals
also congratulated Mr Ahmadinejad. Mohsen Rezai, who won just 1.7% of the vote, declared that Mr Ahmadinejad had been elected president by "legal procedures".
"I will support him in a bid to prevent any delays in the provision of services to the people," Mr Rezai said in a statement.
The president already has the backing of the country's Supreme Leader, Ayatollah Ali Khamenei, who endorsed his election win on Saturday.
Our correspondent says the expressions of support for Mr Ahmadinejad could be an attempt to "lock down" support for the president within Iran's divided political establishment.
The controversy over Iran's election flared after high turnout and long queues at polling stations on Friday led Mr Mousavi's supporters to expect a strong showing from their candidate and a close result.
Turnout was estimated at 85%, with voting extended in many places.
Streets in Tehran were set alight as protesters burned barricades
But official results on Saturday gave the incumbent, Mr Ahmadinejad, a landslide victory. His final share of the vote was almost 63%.
Despite a rapid endorsement of the result from Ayatollah Khamenei, Iran's supreme leader, Mr Mousavi issued a statement denouncing the verdict and alleging widespread voting irregularities.
Our correspondent John Simpson, in Tehran, says the truth about this election may never be known. But many observers in Iran feel that the final result did not reflect the extraordinary numbers of people who turned out to vote, he adds.
World reaction has been muted
, with major powers slow to welcome the Iranian result.
The European Union and Canada have voiced concern about allegations of irregularities, while US Secretary of State Hillary Clinton said only that Washington hoped the result reflected the "genuine will and desire" of Iranians.
Long-time allies such as Venezuela and Syria, as well as neighbours Iraq and Afghanistan, are among those who have recognised Mr Ahmadinejad as the winner.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.