The U.S. and Iran shared cautious optimism Monday following the first round of peace talks in Switzerland, with Vice President JD Vance calling the discussions a "good foundation" for ending the war and the Iranian president praising the degree of consensus reached.

"We laid a very good foundation for a successful final deal," Vance told reporters at the Burgenstock resort in central Switzerland, following negotiations that started Sunday and went on into the night.

"The final deal is the house. 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," he said.

"It's important for all of us to appreciate how much was done, but honestly, there is still a lot to do as we continue to make progress on the nuclear talks, on the economic talks, as we continue to demine the straits and ensure that that flow of traffic continues to pick back up," he added.

"A lot of progress but still some work to do – and we're very committed to doing exactly that," said Vance.

He insisted that the strategic Strait of Hormuz waterway "is open," with "millions and millions of barrels of crude and natural gas flowing through ... that weren't flowing before."

Meanwhile, Iranian President Masoud Pezeshkian, in his first statement following negotiations, lauded the level of consensus and warned against political infighting and divisions at home.

He said that any effort to sow discord would benefit Iran's adversaries

Speaking at a National Tradesmen's Day event in Tehran, Pezeshkian defended Iran's approach to the talks and urged national unity as negotiations continue.

"Any message that leads to division and separation is playing into the enemy's hands," Pezeshkian said, according to Iran's state-affiliated ISNA news agency. "Such a level of consensus has never existed before."

The president said Iran entered the negotiations without making concessions and stressed that Tehran would not retreat from its positions if the other side failed to respect Iran's rights.

Pezeshkian also claimed that the United States had accommodated Iranian requests regarding developments in Lebanon during the diplomatic process and said the talks had produced some positive results, without providing further details.

Vance also confirmed that Tehran has agreed to invite International Atomic Energy Agency inspectors back into the country.

"The Iranians have agreed to invite IAEA inspectors back into their country," he said.

"That is a major milestone for the American people and the first step in permanently denuclearising or permanently ending a nuclear weapons program in Iran," he said.

The negotiators aim to tackle some of the most intractable issues that have dogged U.S.-Iranian relations for decades, including Tehran's nuclear program and enriched uranium.

Under the terms of last week's preliminary deal, released by U.S. officials, Iran will dilute its enriched uranium stocks, possibly by "down-blending on site under the supervision of the IAEA", the U.N.'s nuclear watchdog.

Vance said he expected conversations with the inspectors about their return to Iran to begin imminently.

"I expect that will happen at the minimum this week, but we think even some of those conversations with the inspectors ... and with the IAEA could happen as soon as today," he said.

The first round of Iran-U.S. negotiations, mediated by Qatar and Pakistan in Switzerland, concluded Sunday. The discussions focused on technical aspects of implementing a 14-point memorandum of understanding.

In a joint statement, the Qatari and Pakistani foreign ministries said the parties agreed to establish a high-level committee to oversee the political dimensions of the mediation process in line with the memorandum.

The statement also said the sides had approved a roadmap aimed at reaching a final agreement within 60 days.

Both mediators and Iranian officials separately reported progress in discussions related to the Middle East war and particularly the hostilities in Lebanon.

According to Iranian accounts of the talks, a new mechanism would be created to monitor a cease-fire in Lebanon, and Iran would appoint a representative to participate in that process.

Iranian and U.S. delegations are expected to continue technical discussions in the coming weeks.

The final deal will seek to draw a line under the war launched by the United States and Israel on Feb. 28, which prompted Iran to counterattack with missile and drone salvos across the region – and effectively shut down the Strait of Hormuz, a crucial waterway for the world economy.