Al-Arabiya television reported that Jundollah, a Sunni Muslim rebel group, had claimed responsibility for an attack outside the Imam Hussein Mosque in the south-eastern city of Chabahar, near Iran's border with Pakistan and Afghanistan.
The report could not be confirmed independently.
"Terrorists carried out two suicide bombings among Shia mourners in front of a mosque in the town of Chabahar," Deputy Interior Minister Ali Abdollahi told Iranian radio.
Iran has faced a string of blasts in past months, including two in June that killed 27 people in the same province. Jundollah had also claimed responsibility for that attack.
Iran claims Jundollah has links to Al-Qaeda and has accused Pakistan, Britain and the United States of supporting the group to stir instability in southeast Iran, home to Iran's Sunni minority. The three countries deny backing it.
"Based on our experience, we believe the intelligence services of America and Britain were behind Wednesday's bombing," said senior lawmaker Alaeddin Boroujerdi, the student's news agency ISNA reported.
The Sistan-Baluchestan province is an impoverished area near Pakistan and Afghanistan. Bombings and clashes between security forces, ethnic Baluch Sunni insurgents and drug traffickers have increased in recent years in the area.
In May 2009, a suicide bomber killed 30 people and wounded more than 120 in an attack on a mosque in the city of Zahedan, capital of the Sistan-Baluchestan province.
Ali Mohammad Azad, governor of Sistan-Baluchestan province, put the death toll in the mosque blast at "over 30". "Many women and children were killed in the suicide bombing," he told state television.
Ali Bateni, governor of Chabahar, said two assailants were involved. "One of them was killed and the other was arrested," he said.
Mahmoud Mozafar, head of the province's Red Crescent, said his team had received a number of threats before the ceremony. "We were on alert in the past days because of some anonymous threats," he told Reuters by telephone.
He said that according to his information more than 36 people were killed.
Ethnic Baluch, many with tribal links to their restive kin in neighbouring Pakistan and Afghanistan, make up an estimated one to three per cent of Iran's 77 million people.
Iranian leaders reject allegations by Western human rights groups that the Islamic Republic discriminates against ethnic and religious minorities.