A pathologist cited by the official Irna news agency said 38 bodies had been brought to the town's mortuary, among them women and children. A 39th casualty later succumbed to his wounds, the pathologist said.
The bomber struck in a central square where worshippers were taking part in a procession marking the eve of the last day of Ashura, Red Crescent official Mahmoud Mozafar told the Ilna news agency.
"An individual walked up to some Red Crescent ambulances and blew himself up," he said.
The governor of Sistan-Baluchestan province, Ali Mohammad Azad, said: "Two terrorists were killed, one in the explosion and the second by police."
The prefect of Chabahar, Ali Bateni, said a third terrorist was later arrested.
"There were two terrorists who were spotted before they carried out their attack but one of them managed to detonate his explosive vest," Bateni told Irna.
"The ringleader of this terrorist action has been arrested."
The attack came on the eve of the final day of Ashura, one of the high points of the Shiite calendar when large crowds of worshippers gather in mosques across predominantly Shiite Iran.
But unlike most of the rest of the country, Sistan-Baluchestan where Chabahar is situated has a significant Sunni community and has seen persistent unrest in recent years by the Sunni militants of Jundallah (Soldiers of God).
The group claimed Wednesday's attack, saying it was to avenge the hanging of their leader Abdolmalek Rigi. It identified the two militants as Saiful Rahman Chabahari and Hessan Khashi.
"This operation was a revenge for the hanging of the head of the movement Abdolmalek and other members of Jundallah," the group said on its website junbish.blogspot.com.
"In this suicide operation in the city of Chabahar, tens of guards (members of the elite Revolutionary Guards) and mercenaries have been killed. The operation was carried out to expose the aggressors in Balochistan."
Jundallah, which says it is fighting for the rights of the province's large Sunni ethnic Balochi community, has claimed many deadly attacks on Iranian security forces over the past decade as well as assaults that have led to civilian deaths.
Last month, the United States officially designated Jundallah a foreign terrorist organisation, drawing a cautious welcome from Iran which had previously accused Washington of supporting the group.
Iranian officials renewed the allegation on Wednesday.
The head of parliament's foreign affairs committee, Alaeddin Borujerdi, accused the "intelligence services of the United States and Britain" of being behind the attack, the Isna news agency reported.
Deputy Interior Minister Ali Abdollahi said the "equipment used shows that they are terrorists supported by the intelligence services of the region and the US," Irna reported.
British Foreign Office minister Alistair Burt said he was "appalled" to hear about the suicide bombing and said London "strongly condemns this atrocity".
"I was appalled to hear of today's horrific bomb attack in Iran against pilgrims marking Ashura in the city of Chabahar," the minister for the Middle East and North Africa said in a statement.
"The UK strongly condemns this atrocity. We deplore terrorism in all its forms. Our thoughts are with all those injured and their families."
The 10-day Ashura rituals, which climax in Iran on Thursday, commemorate the killing of Imam Hussain (RA), a grandson of the Prophet Mohammed, by armies of the caliph Yazid in 680 AD. Tradition holds that the revered imam was decapitated and his body mutilated.
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