Iran live updates: Trump says 'no further Naval Blockade,' saying Iran agreed to nuclear inspections

President Donald Trump said on Tuesday that Iranian officials agreed "fully and completely" to allow inspections of its nuclear sites, saying the Strait of Hormuz would remain open as long as Tehran held to those terms.

Iran’s Foreign Minister spokesperson, Esmail Baghaei, said early on Tuesday that Tehran does not "have any plans" to allow International Atomic Energy Agency inspectors to access sites damaged during the war, according to Iranian state media.

Despite Iran's "protestations and false statements to the contrary," officials in Tehran have "fully and completely agreed to highest level Nuclear inspections long into the future (Infinity!!!)," Trump said on social media on Tuesday. "This will insure 'Nuclear Honesty.' If they did not agree to this, there would be no further negotiations!"

"Based on this and other major concessions being made by Iran, I have agreed to allow the Hormuz Strait to remain OPEN, with no further Naval Blockade," Trump added. "However, all ships are remaining in place should it be necessary to reinstitute the Blockade, which seems, at this point, highly unlikely."

Iran and the United States agreed to allow traffic through the strait as part of the terms of the memorandum of understanding signed last week by both countries.

Iran does not "have any plans" to allow International Atomic Energy Agency inspectors to access sites damaged during the war, the spokesperson for Iran’s Foreign Ministry, Esmail Baghaei, said on Tuesday, according to Iranian state media.

"Fundamentally, there is no established protocol for such a situation," he said, according to the Islamic Republic News Agency.

Iran's delegation did not meet with IAEA Director General Rafael Grossi during the U.S.-Iranian talks in Switzerland, IRNA reported.

Vice President JD Vance said on Monday during a news conference in Lucerne, Switzerland, that Iran had agreed to allow the United Nations-affiliated IAEA inspectors to enter their country.

"The Iranians have agreed to invite IAEA inspectors back into their country," Vance told reporters at Bürgenstock, the Swiss resort where the talks were held.

He added, "That is a major milestone for the American people, and the first step in permanently denuclearizing or permanently ending a nuclear weapons program in Iran, and that's exactly what we wanted to do, that's exactly what we asked to happen."

-ABC News' Jamie Dorrington and Fritz Farrow

In addition to speaking with Lebanese President Joseph Aoun, Secretary of State Rubio also held a call with Israeli Prime Minister Benjamin Netanyahu on Friday to discuss “solidifying” a ceasefire and "future talks,” a U.S. official confirmed.

As a result of those calls, the U.S. "started a monitoring mechanism via CENTCOM so that our policymakers have real time and accurate information about fighting in Lebanon,” the official said.

The official also confirmed that another round of talks between representatives of Israel and Lebanon are set to take place in Washington this week over the course of three days.

-ABC News’ Shannon Kingston

Vice President JD Vance left the first days of technical negotiations with Iran projecting optimism, telling reporters as he left Switzerland that he felt "great about the progress that we made."

"The fundamental thing we got is, No. 1, we set up the mechanism to ensure not only the Straits of Hormuz are open, but will stay open," Vance said.

"... No. 2, we actually set up the right mechanism to ensure the regional cease fire to manage the inevitable conflicts that will come up," Vance said.

Vance reiterated his earlier comments in which he said Iran will be allowing IAEA inspectors into the country.

Vance said the U.S. will have to “see” what Iran “actually let[s] the inspectors do” once they are in Iran.

“We have the Iranians allowing weapons inspectors, nuclear inspectors into their country for the first time in a long time. We're obviously going to bolster those inspections, that inspection regime, to make sure they can never have a nuclear weapon,” Vance said.

Inspections were part of the Obama-era agreement that Trump canceled during his first term, after which Iran stopped letting international inspectors in.

-ABC News’ Emily Chang, Hannah Demissie and Michelle Stoddart