Jalal Sayah, the deputy governor of Sistan-Baluchestan, the province bordering Pakistan and Afghanistan where the attack took place, said on Friday: "Hire of the terrorists by the US was verified based on investigation.
"The terrorists, who were equipped by America in one of our neighbouring countries, carried out this criminal act in their efforts to create religious conflict and fear and to influence the presidential election," he told state radio on Friday.
Iranians are due to go to the polls in two weeks to elect a new president.
Ayatollah Ali Khamenei, Iran's supreme leader, blamed "interventionist powers" for trying to incite sectarian conflict with the bombing, and the country's interior minister accused the US and Israel of being behind it.
Ali Reza Rongahi, Al Jazeera's correspondent in Iran, said a Sunni group known as Jundollah had claimed responsibility for several terrorist attacks and abductions in Sistan-Baluchestan in the past.
Iranian state television quoted Arabic news channel Al-Arabiya as saying the group claimed responsibility for the attack on Thursday, but this has not been independently verified.
"Whenever the Islamic Republic needs to prove to the world and the people that it is in control, there are attacks of this kind that aim to prove it cannot maintain peace and calm," Rongahi said.
At least three people, including a child, were also injured in another attack on Friday by armed men at an election campaign office in the same city which run in support of Ahmadinejad.
Mohammad Reza Zahed Sheikhi, who runs the election office, said: "Three knife-wielding people on motorbikes stopped outside the centre on Saadi Street, cursed, made threats and tore up billboards."
He said that as the campaign workers went towards them to protest "the attackers pulled out guns and shot at them".
IRNA, Iran's state news agency, said the attack took place at around 1900 local time (1430 GMT).
Sheikhi said a child was also shot in the stomach and was undergoing surgery.
Two campaign workers sustained arm, stomach and shoulder wounds and were taken to hospital, he said.
"The men ran away, but the police chased and arrested them," Sheikhi said.
Zahedan is the regional capital of the Sistan-Baluchestan province which borders Pakistan and Afghanistan.