The remarks were consistent with 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.
Iran said on Wednesday that Washington had agreed to remove all sanctions on Iran's oil and shipping, and take some senior figures off a blacklist, at talks to revive Tehran's 2015 nuclear deal with global powers which are now on a pause.
The remarks, by outgoing president Hassan Rouhani's chief of staff, were consistent with 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 head of Iran's judiciary who is on the 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," presidential chief of staff Mahmoud Vaezi was quoted as saying by Iran's state media.
"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. 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. Other Western and Iranian officials have also said the talks are a long way from a conclusion.
Iran agreed in 2015 to curbs on its nuclear programme in return for the lifting of international sanctions. Trump abandoned the agreement three years later and reimposed sanctions, and Tehran responded by violating some nuclear limits.
The new U.S. administration of President Joe Biden
aims to restore the deal, but the sides disagree on which steps need to be taken and when.
Iranian and Western officials alike say Raisi's rise is unlikely to alter Iran's negotiating position, as Supreme Leader Ayatollah Ali Khamenei already has final say on all major policy.
However, some Iranian officials have suggested Tehran may prefer an agreement before Raisi takes office to give the new president a clean slate.