Vice President JD Vance on Monday said after the U.S. and Iran struck a preliminary deal that "a lot" of details remain to be ironed out, but he expressed confidence that America has "all the cards" in subsequent talks.

Vance told CNBC's "Squawk Box" that Iranian foreign minister Abbas Araghchi is expected to be involved in those upcoming discussions — as well as its parliamentary speaker, Mohammad Bagher Ghalibaf, a hard-liner whose participation could signal that the regime's conservative faction is on board with the deal.

The agreement reached Sunday would extend the U.S.-Iran ceasefire for 60 days and set up a framework for future negotiations about Tehran's nuclear program and other key issues. The text of the preliminary deal has not been released.

A senior U.S. official told reporters later Monday that President Donald Trump, Vance and Ghalibaf have already signed the deal in the form of a memorandum of understanding.

An official signing ceremony is set for Friday in Geneva.

The details of the agreement will be made public within 24 to 48 hours, another U.S. official said, speaking on condition of anonymity to discuss deal terms that haven't been made public. But Trump, after traveling to France for the annual G7 summit, said he expected the MOU text to come out "sometime after Friday."

Vance told CNBC on Monday morning that the deal's two major prongs are reopening the Strait of Hormuz and clinching a long-term commitment that Iran will never develop a nuclear weapon. Trump has repeatedly stated that the war was started in order to prevent Iran from obtaining a nuke.

Vance indicated that if Iran abides by the deal's commitments, it will be rewarded with loosened economic sanctions or other barriers, allowing Tehran "to be reinvited into the world economy."

"I think it's a great day for the American people," said Vance, who has been involved in negotiations with Iran throughout the war that began Feb. 28.

Iranian state media on Monday reported that Araghchi said a meeting will "probably" take place on Friday in Switzerland, where the two sides will officially sign the MoU and hold the first round of negotiations.

The vice president told CNBC earlier Monday morning that despite the deal's 60-day timer, "our expectation is that the strait is going to be opened in a toll-free way for the long term."

"That's the sort of thing that we're going to figure out in these technical negotiations," he said.

"There are a lot of very important details to figure out that we're actually going to sit at the table and discuss together and figure out a path forward on these details," Vance said.

Those to-be-determined details aren't limited to the strait. Vance said that while Iran has "committed to destroy and dispose of their stockpile of highly enriched material," the process for doing so has not been established.

"And what we've said is, 'OK, let's talk about how exactly we're going to do that,'" he said.

"They want access to an unsanctioned economy. We've talked about, 'OK, we're open to that,' but that would require a long-term commitment to the inspection and verification regime" imposed under the deal, he went on.

"So, a lot of these details are going to be figured out during those 60-day talks," he said.

"We feel quite confident that we're in a strong position," he added.