US Vice President JD Vance said on Monday in Switzerland that progress has been made in talks with Iran, with Tehran agreeing to allow nuclear inspectors into the country and conversations over the inspections possibly beginning as soon as this week.

Speaking after talks in Switzerland, ​Vance also cited ​a mechanism to keep the Strait ‌of ⁠Hormuz open, with technical talks set to continue in the ​days and ​weeks ⁠to come.

Conversations over nuclear inspections in ​Iran could start ​as ⁠soon as this week, he said.

Vance further said peace talks with Iran created a "good foundation for a successful final deal" to end the war that began at the end of February.

"The final deal is the house," Vance told reporters. "We set the foundation. We haven't built the house, but we've laid a successful foundation to get to a good place for the American people."

Vance's comments came after he and Iran's parliamentary speaker Mohammad Bagher Qalibaf on Monday wrapped up a lengthy round of initial talks aimed at solidifying a permanent end to the war between the countries.

The vice president also suggested that the US administration could agree to unfreeze Iranian assets for purchases of US soy, corn and wheat.

The mediation effort in Switzerland, which started Sunday and stretched into the early hours of Monday, had rocky moments. But the talks also led to some agreements between the two sides.

Earlier in the day, the two sides agreed to a roadmap ‌towards a lasting deal to end their war within 60 days at the talks in the Qatari-owned Swiss mountain resort of Buergenstock, which concluded early on Monday, mediators Pakistan and Qatar said.

They also agreed on a mechanism to end fighting in Lebanon between US ally Israel and Iran-aligned Hezbollah, and opened a communications line to help ensure safe passage for commercial ships through the strait, a vital global oil supply route.

Sunday's meeting followed an interim deal signed last week and ​stretched into the early hours of Monday, despite Tehran again shutting the waterway on Saturday and US President Donald Trump threatening to resume attacks on Iran.

"The discussions were held in a ​positive and constructive atmosphere and yielded encouraging progress," Pakistani Prime Minister Shehbaz Sharif wrote on X, adding that the first round of talks had "concluded successfully".

Vice ⁠President JD Vance, who led Washington's delegation, told reporters Trump had "asked us to turn over a new leaf to transform our relationship with the people of Iran" and said progress had been made towards ​ending hostilities in Lebanon.

"These things are always a little bit messy," he said.

The talks began under the terms of the memorandum of understanding reached last week to extend a tenuous ceasefire from April for at least another 60 days.

Before the talks officially began, Fox ‌News quoted ⁠Trump as saying he had told Iranian officials "you won't have a country" if they tried to close the strait again. Trump also reiterated an earlier threat that the US would take over the waterway and possibly charge a toll of its own, Fox News said.

Iran's semi-official Tasnim news agency, citing an informed source, said that after Trump's threats became public, the Iranian delegation refused to return to the room where talks were held, though messages were traded via the mediators.

According to Tasnim's source, the Iranians said the start of negotiations on nuclear matters required the delivery of other parts of the MOU, including the release of ​frozen assets and US waivers authorizing Iranian oil ​exports.

The interim agreement calls for reopening the Strait ⁠of Hormuz and ending all hostilities, including in Lebanon, where violence continued after a ceasefire was declared on Friday.

Accusing the US of failing to meet its commitment to halt fighting in Lebanon, Iran said at the weekend that it had again stopped maritime traffic through the strait.

Five vessels passed through the strait ​on Sunday, a sharp drop from the 26 ships spotted a day earlier, data from analytics firm Kpler showed. The data may exclude vessels ​that switch off their transponders ⁠while travelling in the Gulf.

The violence between Hezbollah and Israel has abated since late on Saturday.

Security sources in Lebanon said Israel's last airstrike was on Saturday evening, and that the lull in violence was the longest since Hezbollah opened fire in support of Iran on March 2 although an Israeli drone could be heard over Beirut.

Reflecting reduced tensions, the Israeli military lifted safety restrictions in eight communities near the Lebanese ⁠border beginning at ​6 a.m. (0300 GMT) on Monday.

Lebanese President Joseph Aoun discussed efforts to maintain the ceasefire and halt Israeli military escalation during ​a phone call with Vance, Qatar's prime minister and White House envoy Jared Kushner, the Lebanese presidency said.

Israeli President Isaac Herzog said Israel was not opposed to a diplomatic end to the Iran war, but any agreement must ensure Tehran cannot use ​funds it receives as part of the deal for military purposes or to support regional proxies.