Negotiators have made significant progress in the last week or so on reviving the 2015 Iran nuclear deal but very tough issues remain, a senior U.S. State Department official said on Friday.

The U.S. official said he hoped Iran's lead negotiator would return in the coming days to Vienna, where the talks are taking place, "with a positive view" but that even if he did, there were still difficult issues on the table.

"There's been significant progress over the last week or two," the U.S. official told reporters on condition that he not be named. "But at the same time it's important to note that very serious issues remain."

The broad aim of the talks is to return to the original 2015 bargain of lifting sanctions against Iran, including those that have slashed its oil sales, in exchange for restrictions on its nuclear activities that extend the time Tehran would need to make enough enriched uranium for an atomic bomb if it chose to.

Iran has long denied such an ambition and has said that its nuclear program is solely for peaceful purposes.

The U.S. official said a deal, if one can be reached, would in many ways track the terms of the original accord on Iran's levels of uranium enrichment, the stockpile of enriched uranium it may hold, and the numbers of centrifuges it may operate.

However, he left open the possibility of some modifications to account the additional sanctions that then-President Donald Trump imposed on Iran after pulling the United States out of the deal in 2018 and the nuclear advances that Iran has since made.

"We hope that when Iran comes back, it comes back in with a pre-disposition to try to resolve this quickly," the official said, saying there were still disagreements "for which there is not a solution that's on the table."

He declined to name the sticking points, and would not be drawn on whether Washington had persuaded Tehran to agree to follow-on negotiations on its nuclear program, its development of ballistic missiles or support for regional proxies.

He also said there has not been any deal reached in separate negotiations about the release of four U.S. citizens whom the United States believes have been wrongfully detained by Iran.