"The first meeting, was positive, constructive, compelling," Steve Witkoff, who led the US delegation to talks last week in Oman, said in a televised Fox News interview.

Witkoff appeared to stop short of calling for a complete dismantling of Iran's nuclear program, saying "this is going to be much about verification on the enrichment program."

"They do not need to enrich past 3.67 percent," the real estate magnate said, referencing the maximum level allowed under the prior nuclear agreement that Trump exited during his first term, in 2018.

"In some circumstances, they're at 60 percent, in other circumstances 20 percent," Witkoff said. "That cannot be, and you do not need to run, as they claim, a civil nuclear program where you're enriching past 3.67 percent."

The multi-party 2015 deal that Trump abandoned aimed to make it practically impossible for Iran to build an atomic bomb, while at the same time allowing it to pursue a civil nuclear program.

The latest International Atomic Energy Agency said Iran had an estimated 274.8 kilograms of uranium enriched to 60 percent, nearing the weapons grade of 90 percent.

Verification of "weaponization" capabilities will be another "critical" point in the negotiations with Iran, Witkoff said.

"That includes missiles, the type of missiles that they have stockpiled there, and it includes the trigger for a bomb," he told Fox host Sean Hannity.

"The devil will be in the details" of any formal document, he said, adding "hopefully we'll have that high quality problem of getting a document drafted."

"But verification will be the key point that undergirds this agreement."