The explosions on Sunday morning targeted several public buildings in Ahvaz, an ethnic Arab-majority city close to the border with Iraq and capital of the oil-rich Khuzestan province.
Aljazeera reported that the buildings were damaged by the blasts, adding that no group had claimed responsibility so far.
The province's deputy governor, Gholam Reza Shariati, told state television that unidentified attackers were trying to "attack the territorial integrity of the country and damage the election process".
Iran is to go to the polls to elect a new president on Friday.
Shariati put the toll at five and said 80 were hurt. State television, quoting medical sources, said eight people were killed in the Ahvaz bombings.
Interior Ministry spokesman Jahanbaksh Khanjani said one of the blasts - the first on Iranian soil in several years - was from a car bomb outside the Ahvaz prefecture.
Iran's state-run television reported later on Sunday that two people were killed and three injured in an explosion in central Tehran, hours after the Ahvaz blasts.
The explosion was followed by a series of smaller blasts.
No further details were immediately available about the Tehran blast, which occurred near the Imam Hussein Square in the city centre.
A top national security official, Ali Agha Mohammadi, blamed "terrorists" and Arab separatists sheltered by US troops in neighbouring Iraq for the blast.
He said that an ethnic Arab separatist group had claimed responsibility for the quartet of bomb blasts in Ahvaz.
"The terrorists of Ahvaz infiltrated Iran from the region of Basra" in southern Iraq, Mohammadi said. "These terrorists have been trained under the umbrella of the Americans in Iraq."
He said Iran suspected British troops based across the border in southern Iraq might also have links to the group, but added: "We are not certain."
There has been no reaction to the comments thus far.
List of targets
The explosions occurred between 9am and 11am. State television pictures showed the ground around the blast site strewn with broken glass, rubble and pools of blood.
"One of the bombs was inside a car parked outside the prefecture," Mohammad Kianoush-Rad, a former parliament deputy, said.
Akbar Hashemi Rafsanjani leads
Friday's election predictions
"Two others exploded in the Amaniyeh administrative district. A local housing ministry building was hit. The fourth exploded in the Padadshahr residential district.
"The number of injured is very high, and an appeal has been made for blood donors," Kianoush-Rad added.
Quoted by the state Islamic Republic News Agency (Irna), the Interior Ministry's security affairs director Amir Hossein Motahar said one of the blasts was outside the home of the director of Iranian state television operations in Ahvaz.
One bomb also exploded while police were trying to defuse it, he said.
Irna said one of the bombs appeared to have been hidden in the toilets of one of the buildings, the inside of which was shown on television to have been almost gutted.
"I heard a huge explosion," a witness, Anush Darihaki, said. "All the roads near the explosions were sealed off by police. All the windows in the areas were shattered.
"I have no idea who could have done this," he added.
Ahvaz, about 500km southeast of Tehran and 50km from the border with Iraq, was rocked by ethnic violence between 15 and 18 April.
According to official figures, five people were killed in those clashes, which appeared to have been sparked by a forged letter, dating back seven years and attributed to then vice-president Mohammad Ali Abtahi, calling for modifications to Khuzestan's ethnic composition.
Ahvaz is about 50km from the
border with Iraq
Tehran blamed foreigners and counter-revolutionaries for the ethnic tensions but admitted the province's development was still hampered by the devastation it suffered during the 1980-1988 war with Iraq.
On Friday, Iran is to go the polls to elect a successor to reformist President Mohammad Khatami.
Informal opinion polls in the Iranian press suggest that none of the eight candidates will be able to secure more than 50% of the vote needed to win. That means the top two would have to go into a run-off - unprecedented in the 26-year history of the Islamic republic.
Tipped as the frontrunner among the eight candidates is powerful former president Akbar Hashemi Rafsanjani, a pragmatic conservative.
Aljazeera has learned that his electoral campaign managers have been wooing young voters, going so far as to stage a musical event - a first in Iran's recent political history.
Trailing him are the main reformist candidate Mostafa Moin and the hardline former national police chief, Mohammad Baqer Qalibaf.
Observers say half the country's voters may not turn out to cast their ballots, in a reflection of public disappointment with the outgoing Khatami's unfulfilled reform promises.