"They also promised to give us a base along the border with Afghanistan near Iran."
He said that US officials met him in Pakistan around March 2009 and had also sought a meeting "after the last major operation we took part in".
Jundallah claimed responsibility for an attack in the town of Pisheenin October 2009 that killed 42 people, including seven Revolutionary Guard commanders and several tribal leaders.
US officials earlier dismissed claims by Heydar Moslehi, the Iranian foreign minister, that Rigi had visited a US military base just 24 hours before his arrest on Tuesday.
"Iranian claims that Abdolmalek Rigi was at a US military installation prior to being apprehended are absolutely false," Geoff Morrell, the Pentagon press secretary, said.
"Allegations that we played some role in creating or supporting Jundallah is just another false claim in a long list of ridiculous Iranian fabrications"
Pentagon press secretary
He said that accusations that Washington supported Jundallah or any other anti-goverment groups fighting in Iran were "nothing more than Iranian propaganda".
"Allegations that we played some role in creating or supporting Jundallah is just another false claim in a long list of ridiculous Iranian fabrications."
Iran has repeatedly accused the United States, Britain and Israel of inciting unrest by supporting opposition to the government of the Ismaic republic.
Jundallah says it is fighting to secure rights for Iran's Sunni Baluchis, who form a significant population in Sistan-Baluchestan, along the border with Afghanistan and Pakistan.
Pakistan said earlier in the week that it aided Rigi's arrest, but gave no details of the support it provided.
Tehran has previously criticised Pakistan for allegedly allowing Jundallah to operate out of Pakistan's Baluchistan province.
The latest accusations come as Washington increases the pressure on Tehran over it decision to further enrich its uranium stockpile, a move it says shows that Iran has rejected a united Nations-backed deal to resolve the stand-off over it nuclear programme.
The US and it allies have said that they believe the programme is a cover for developing an atomic weapon, but Iran insists that its motives are entirely peaceful.