The Iranian remarks, by outgoing President Hassan Rouhani's chief of staff, echoed previous assertions by officials in Rouhani's pragmatist camp that Washington is prepared to make major concessions at the talks, under way since April in Vienna.
The talks adjourned on Sunday for a break, two days after Iran held a presidential election won by hardliner Ebrahim Raisi, the Iranian judiciary chief who is on a U.S. blacklist. Raisi is due to replace Rouhani in August.
"An agreement has been reached to remove all insurance, oil and shipping sanctions that were imposed by (former U.S. President Donald) Trump," Rouhani's chief of staff Mahmoud Vaezi was quoted as saying by Iranian state media.
Like other Western and Iranian negotiators who have said the talks remain a long way from conclusion, German Foreign Minister Heiko Maas said on Wednesday that Tehran and the powers still had to overcome significant hurdles.
"We are making progress but there are still some nuts to
crack," Maas told a joint news conference with U.S. Secretary of
State Antony Blinken. Maas said a deal was possible even after the election of Raisi, an implacable critic of the West.
U.S. National Security Adviser Jake Sullivan said on Sunday there was still “a fair distance to travel”, including on sanctions and on the nuclear commitments that Iran has to make to salvage the tattered deal.
Iran agreed in 2015 to curbs on its uranium enrichment programme, a possible pathway to nuclear weapons, in return for the lifting of international sanctions. Trump abandoned the agreement three years later, calling it flawed to Iran's advantage, and reimposed harsh sanctions that hammered Iran's economy.
Tehran responded by violating some enrichment limits, while continuing to insist that it has no nuclear arms ambitions.
Iranian and Western officials alike say Raisi’s ascendancy is unlikely to alter the Islamic Republic’s negotiating position, as clerical Supreme Leader Ayatollah Ali Khamenei already has the final say on all major policy.
Vaezi said the United States had agreed to take some senior Iranian figures off a blacklist.
"About 1,040 Trump-era sanctions will be lifted under the agreement. It was also agreed to lift some sanctions on individuals and members of the supreme leader's inner circle."
U.S. President Joe Biden's administration aims to restore the deal, but the sides disagree on which steps need to be taken and when to defuse mutual suspicions and ensure full compliance.
But some Iranian officials have suggested Tehran may prefer an agreement before Raisi takes office to give the new president a clean slate and avoid blame if problems subsequently arise.