The moderate Parlemannews website said supporters of Montazeri, an architect of the 1979 Islamic revolution that toppled the US-backed shah, were flocking to the Shiite Muslim holy city of Qom to attend his funeral on Monday.
The reformist Tagheer website reported that pro-opposition Iranians were gathering in squares of Tehran on Sunday to mourn his death, and that riot police were seen in different parts of Qom, where Montazeri lived and died.
His death from a heart attack, reported by official media on Sunday, coincides with tension rising once again in the Islamic Republic, six months after the presidential poll plunged the major oil producer into political crisis.
"My grandfather died in his sleep last night. People and friends are coming to express their condolences but there are no special security measures around our house," Naser Montazeri told Reuters by phone from Qom, some 125 km (78 miles) south of Tehran.
Ayatollah's body in Qom, Sunday (Photo: AFP)
Monday's burial, to start at 9 am (0530 GMT), could become a rallying point for the reformist opposition and this may worry the authorities, said London-based Iran analyst Baqer Moin.
"The amount of support shown to him will hearten the opposition who are mourning his loss," Moin said.
Parlemannews said Montazeri followers were travelling from other parts of Iran to Qom, a Shiite Muslim religious centre. "Thousands of people from Isfahan, Najafabad and other cities are going to Qom to attend Montazeri's funeral," it said.
Tagheer, the website of pro-reform cleric Mehdi Karoubi, said Montazeri supporters were gathering in Tehran.
"The social network of the reform movement has called on its supporters to gather in Mohseni square to mourn ... based on reports people have already gathered in some other squares in Tehran," it said.
Video posted on the Internet showed hundreds of people gathering to mourn Montazeri at universities in Tehran and footage of a large gathering of people which the poster said was shot in the central city of Najafabad, Montazeri's birthplace.
"Montazeri, congratulations on your freedom," the crowd in Najafabad chanted, and "oppressed Montazeri, we will follow your path."
Montazeri was named in the 1980s to succeed revolutionary leader Ayatollah Ruhollah Khomeini as Iran's top authority, but fell out with him over the mass execution of prisoners.
'Fruit of my life'
One of Iran's most senior clerics, he spent five years under house arrest until 2002 but remained a leading opposition voice until his death, even though he rarely left his home in Qom.
"He will be remembered as a man who sacrificed his political position for the sake of his principles," said Moin, describing him as an inspiration for other pro-reform clerics.
Montazeri, who was a close ally of Khomeini before the revolution and jailed several times by the shah's police, was among the government's harshest critics in a clerical establishment where splits have widened during the turmoil triggered by June 12 vote.
In August, the ayatollah said on his Web site that the authorities' handling of street unrest following the election "could lead to the fall of the regime" and he denounced the clerical leadership as a dictatorship.
The pro-reform opposition says the poll was rigged to secure hardline President Mahmoud Ahmadinejad's re-election.
The authorities have denied the charge and portrayed the huge opposition protests after the election, which were quelled by the elite Revolutionary Guards and Islamic militiamen, as a foreign-backed bid to undermine the clerical leadership.
Thousands of opposition supporters were detained after the vote, including senior reformers. Most have been freed but more than 80 people have received jail terms of up to 15 years and five have been sentenced to death over the post-vote unrest.
Tension increased earlier this month when pro-opposition students clashed with the security forces armed with batons and tear gas in the biggest anti-government protest in months.
Official media initially did not give prominent coverage to Montazeri's death, but it topped state television's main afternoon broadcast.
Khomeini once called Montazeri the "fruit of my life", but the official IRNA news agency said "problem elements" in Montazeri's household and his statements "appreciated by enemies of the Islamic Republic" were to blame for his estrangement with Khomeini two decades ago.
Instead of Montazeri succeeding Khomeini upon the death of the Islamic Republic's founder in 1989, current Supreme Leader Ayatollah Ali Khamenei became the country's highest official.