"The first explosion took place behind a checkpoint and a number of Revolutionary Guard members were killed and injured because of it."
The attack came as people celebrated the birthday of Imam Hussein, grandson of the Prophet Mohammed, a day also set apart each year to honour the Revolutionary Guards.
Jundallah says it is fighting for the rights of the Sunni Baluch minority, and accuses Iran's Shia-dominated government of persecution.
The blasts follow the hanging by Iran in June of Abdulhamid Rigi, the group's leader, in Zahedan after he was found guilty of carrying out attacks against civilians, armed robbery, and engaging in a disinformation campaign against Iran.
His younger brother, Abdulhamid, was executed in May in Iran after being captured in Pakistan in 2008 and extradited to Iran.
Hossein Ali Shahriari, a Zahedan member of parliament, told Fars that there were two suicide attacks one after another, with the first one carried out by a bomber dressed as a woman.
"The attacker, dressed in women's clothing, was trying to get in the mosque, but was prevented" when the first blast took place, Shahriari said.
"When people came to rescue those hit in that blast, another bomber blew himself up. Three to four have been killed at least in the first attack."
Jundallah has previously carried out several deadly attacks in Sistan-Baluchestan- including on the elite Revolutionary Guardscorps.
Aminullah Habibi, a security analyst and a research fellow at the UK Defence Academy, in London said the "message" the attackers wanted to convey is that "they still have the capacity and power to inflict damage to the Revolutionary Guards".
"The fact of the matter is that they [Iranian authorities] have responded heavily and ... have executed a lot of their members," Habibi told Al Jazeera.
"But the problem is that Baluchestan and Zahedan is located in a very volatile area in terms of its border with Pakistan and Afghanistan.
"Some of these militants are just crossing the border, and they are linked to other sources of income like drug or people trafficking.
"And they also have sanctuaries on the other side of the border; they can go and come back .... They've changed their tactic by the way. It's very difficult for the Revolutionary Guards to stop them."
The United States described the attacks as "horrific", and called for the perpetrators to be held accountable.
"I condemn in the strongest possible terms today's terrorist attacks claimed by Jundallah that targeted Iranians at a mosque in the Sistan-Baluchestan province of Iran," Hillary Clinton, the secretay of state, said in a statement.
"The United States extends its sympathy to the families and loved ones of those injured and killed.
"We also call for the perpetrators of this horrific attack to be held accountable for their actions.
"This attack, along with the recent attacks in Uganda, Pakistan, Afghanistan, Iraq, and Algeria, underscores the global community's need to work together to combat terrorist organisations that threaten the lives of innocent civilians all around the world."