Live Updates: U.S.-Iran deal signing gets more ships moving in Strait of Hormuz, but big challenges remain

Nearly 4,000 people have been killed in Lebanon by Israeli operations against Iranian-backed Hezbollah, according to Lebanon's Ministry of Public Health.

Since March 2, when Israel launched major attacks in Lebanon in response to Hezbollah's rocket and drone fire at Israel in retaliation for the joint U.S.-Israeli war on Iran, at least 3,912 people have been killed and 11,873 others wounded, the ministry said Thursday.

The memorandum of understanding signed Wednesday by the U.S. and Iranian presidents calls for an immediate halt to fighting on all fronts, including in Lebanon, and Iran has said Israeli forces remaining in the neighboring nation would be considered a violation of the deal.

Israel's military said Thursday, however, that forces would remain in Lebanon and continue operating against Hezbollah.

Defense Secretary Pete Hegseth warned Thursday that the U.S. military stood ready to reimpose its naval blockade of Iran's ports and vessels if the Iranian regime doesn't adhere to the agreement signed Wednesday by President Trump and Iranian President Masoud Pezeshkian. 

"If Iran doesn't comply, then we're more than able to reimpose an ironclad blockade," Hegseth told reporters during a visit to the NATO headquarters in Brussels, Belgium.

"If underneath the timeline of these talks Iran does not do what it says it's going to do, just give up nuclear weapons, give up nuclear ambitions, give away their nuclear material, close nuclear facilities, then the War Department is here and prepared to restart if we need to," Hegseth said.

President Trump lashed out at critics of his agreement with Iran on Thursday, calling those who accused him of not being "tough" on Iran "fools," ahead of negotiations in Switzerland aimed at reaching a broader deal to end the war.

"These fools, who think I haven't been tough enough on Iran, when the Stock Market Just Hit A RECORD HIGH, and Oil prices are 'tumbling' down, are either jealous, bad people, or stupid," Mr. Trump posted on social media hours after signing the deal.

Oil prices have tumbled since Mr. Trump first announced an agreement with Iran. The memorandum signed Wednesday calls for the immediate reopening of the Strait of Hormuz, but leaves negotiations on Tehran's nuclear program and the lifting of Western sanctions for the next, 60-day phase of talks.

Iran's foreign minister said the next phase of the U.S.-Iran deal will be more difficult than reaching the memorandum of understanding signed Wednesday.

"Our work is now more difficult than before, because implementing international agreements is always far more difficult than drafting them," Esmail Baqaei said in a statement published by Iran's state broadcaster IRIB.

The minister also said ships were already moving in and out of Iranian ports "without any problems," as a result of the U.S. lifting its naval blockade. 

Switzerland's government confirmed Thursday that "initial negotiations" under the U.S.-Iran agreement were set to begin at a Swiss lakeside resort on Friday.

"Currently, the plan remains for the United States and Iran, along with the mediators Pakistan and Qatar and other involved countries, to meet tomorrow at the Burgenstock for initial negotiations on the implementation of the agreement," the Swiss foreign ministry said in a statement.

The announcement lifted a veil of uncertainty that had hung over the meeting at the Burgenstock luxury hotel complex near Lucerne in central Switzerland, initially announced on Tuesday.

At the time, it had been billed as a signing ceremony of the memorandum of understanding, but the signing was unexpectedly moved forward, with President Trump laying down his signature Wednesday at a candlelit dinner outside Paris, as Iranian President Masoud Pezeshkian signed remotely.

The Israeli military said Thursday that forces deployed in southern Lebanon would remain there, and "continue to remove threats" and strengthen defenses in the area.

In a statement, the Israel Defense Forces said troops would stay in the "security zone" - an area spanning Lebanon's southern border with Israel and extending about six miles into the country.

"IDF soldiers are stationed in the designated area of operation in southern Lebanon, and will continue to remove threats and strengthen the defense of Israel's northern residents," Israel's military said.

Iran's foreign minister said earlier this week that if Israeli forces remain in Lebanon, it would be considered a violation of the U.S.-Iran deal, which calls explicitly for "the immediate and permanent end to military operations on all fronts, including in Lebanon." 

At least 10 commercial vessels were tracked transiting the Strait of Hormuz Thursday morning, and six more appear to be heading in the same direction to exit the Persian Gulf.

It's a noticeable increase in traffic, but still far below the pre-war average of around 135 ships per day moving through the vital waterway, which is the only route in and out of the Gulf.

Among the ships is a French-flagged liquified natural gas (LNG) carrier, Mraikh, which is operated by QatarEnergy. A ship carrying vehicles owned by Italian logistics company Grimaldi Group was also making the crossing, months after dropping off its cargo at Persian Gulf ports. Both ships were among the hundreds stuck in the Persian Gulf since the start of the war, according to data from MarineTraffic.com.

Cargo ships and oil tankers owned by Hong Kong and Chinese companies were still broadcasting that they had Chinese crew on board, a tactic adopted by mariners at the start of the conflict when Iran said it would target ships linked to the U.S. and Israel.

Several sanctioned Iranian tankers that crossed the U.S. naval blockade line earlier in the week were still en route to Iranian ports Wednesday morning.

Israel is holding negotiations with the U.S. as it seeks to keep troops deployed in southern Lebanon, according to two Israeli officials quoted by the Reuters news agency.

The deal struck between the U.S. and Iran calls for the "permanent termination of military operations on all fronts, including in Lebanon." 

While Israel is not explicitly named in the agreement, the continued presence of its troops in southern Lebanon is considered by Iran to be a violation of this clause.

A senior Israeli official told Reuters on Thursday that Israel was "conducting stubborn negotiations" with the U.S. over the deployment of its forces in southern Lebanon.

Prime Minister Benjamin Netanyahu's office did not respond when contacted by CBS News for comment on the report.

The Israeli military announced on Thursday that one of its soldiers had been killed in fighting in southern Lebanon the day before in an incident that also wounded seven soldiers.

Master Sgt. Alexander Filin, 29, "fell in combat," the military said in a brief statement, adding that an officer, a reserve officer and a reserve soldier were moderately wounded.

A combat non-commissioned officer, two reserve soldiers and a female reserve soldier were lightly wounded, the military added.

The United States and Iran signed a memorandum of understanding on Wednesday meant to end the Middle East war, with fighting halted on all fronts, including in Lebanon.

Lebanon was drawn into the conflict when Tehran-backed Hezbollah fired rockets at Israel on March 2 in support of Iran.

Lebanon said earlier that Israel's massive campaign of airstrikes and ground invasion has so far killed more than 3,800 people.

Israel's side saw 31 soldiers and one civilian contractor killed since March 2.

The U.S.-Iran memorandum of understanding will take "immediate effect" now that the presidents of both countries have signed it, said Pakistani Prime Minister Shebhaz Sharif, who helped mediate talks between the two sides.

Sharif also wrote on X that "as a first step, Islamic Republic of Iran will instantly reopen the Strait of Hormuz and the United States of America will immediately lift the naval blockade."

"The signing of this agreement at the highest level of the respective governments demonstrates the commitment of both sides to a diplomatic resolution of the conflict," he said.

President Trump and Iranian President Masoud Pezeshkian signed the memorandum of understanding on Wednesday, a U.S. official told CBS News. Mr. Trump later told reporters that he signed the deal in Versailles while taking part in a reception hosted by French President Emmanuel Macron after attending the G7 summit. 

In Iran's system of government, the most powerful official is not the president, but Supreme Leader Mojtaba Khamenei.