Talks between the U.S. and Iran have made "great progress" despite "threatening" and "whining," U.S Vice President JD Vance has said.

Speaking on Monday, Vance said the talks in Bürgenstock, Switzerland, were continuing and Tehran had agreed to permit International Atomic Energy Agency inspectors back into Iran. The talks were strained over the weekend when Iran announced it had closed the Strait of Hormuz over Israeli strikes on Lebanon, saying these violated the ceasefire.

"Yes, there was a little bit of threatening, there was a little bit of whining, but at the end of the day, the talks continued, and we made great progress," Vance told reporters.

Vance said Iran's agreement for IAEA inspectors to return to their country was "a major milestone for the American people, and the first step in permanently denuclearizing or permanently ending a nuclear weapons program in Iran."

Looking ahead, Vance said a process is now in place to ensure that escalation in the region can be avoided.

"We want a regional ceasefire. We want Hezbollah to stop firing at our friends in Israel. We want Israelis to be able to live in peace. We also want to make sure that, when things happen, they don't spiral into a broader escalation, and so we've been, I think, very good at setting up what we're calling a deconfliction mechanism," he added.

Earlier, Iran's foreign minister, Abbas Araghchi, said the talks had yielded "major progress."

Vance said that while a "very good foundation for a successful final deal" had been laid, he said that there is "still a lot to do," particularly around the demining of the Strait of Hormuz, to help ensure the flow of traffic picks up.

Shipping through the critical waterway — through which about roughly 25% of the world's total energy supply is transported — stalled over the weekend, according to maritime data trackers, after Tehran announced it had again closed the key oil choke point.

Vance added that Jared Kushner, President Donald Trump's son-in-law, had come up with "a very interesting solution" along with the Qataris, where the U.S. would have approval over the process of the unfreezing of any frozen Iranian assets.

"What Jared and the Qataris and the entire team here in Bürgenstock accomplished is to me a classic Trump deal, where if Iranian assets are ever unfrozen, they're going to go to make American farmers richer and to feed the Iranian people," Vance said.

"That's a very, very good and very classic Trump deal. That's great for our people, great for the people of Iran, and fundamentally, again, will contribute to this regional security architecture that we've built."