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

Strait of Hormuz crossings nearly tripled week-on-week as traffic rebounds sharply after the signing of a memorandum of understanding between the U.S. and Iran, according to Marine Traffic and Kpler data.

"According to #MarineTraffic data and Kpler data, confirmed crossings rose from 32 vessels between 12–14 June to 93 vessels between 19–21 June, an increase of 61 crossings week-on-week. The sharpest change came on Saturday, when crossings jumped from 3 to 42 compared with the previous weekend," according to Marine Traffic.

The International Maritime Organization announced an evacuation plan for over 11,000 seafarers stranded in the region, saying it has secured the "necessary safety guarantees and have thoroughly verified the conditions for safe navigation to support these operations."

"This large-scale operation will be carried out in close cooperation with Iran, Oman, all other coastal States in the region, the United States and the maritime industry," IMO Secretary-General Arsenio Dominguez said in a statement.

"After months of hardship and distress for thousands of innocent seafarers, and negative impact for the whole world, I welcome with deep satisfaction the peace agreement concluded between the United States and Iran, marking a decisive step towards restoring maritime security and bringing to an end the unacceptable attacks against civilian shipping," Dominguez said.

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