Signing of the US-Iran deal gets more ships moving through the Strait of Hormuz, but major challenges remain

President Trump lashed out at critics of his Iran deal on Thursday, calling those who accused him of being “tough” on Iran “fools,” ahead of talks in Switzerland aimed at reaching a comprehensive deal to end the war.

“These idiots, who think I wasn't strong enough in Iran, when the Stock Market just hit a RECORD HIGH, and oil prices are 'falling', they can be jealous, bad people, or stupid,” Mr. Trump wrote on social media hours after signing the deal.

The price of oil has fallen since Mr. Trump first announced the deal with Iran. The memorandum signed on Wednesday calls for the immediate reopening of the Strait of Hormuz, but leaves talks on Tehran's nuclear program and the lifting of Western sanctions for the next, 60-day phase of negotiations.

Iran's foreign minister said the next phase of the US-Iran deal will be more difficult than reaching the cooperation agreement signed on Wednesday.

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

The minister also said that ships were already going in and out of Iranian ports “without problems,” because the US lifted its shipping embargo.

The Swiss government confirmed on Thursday that “preliminary talks” under the US-Iran deal were to begin in the Swiss lakeside resort on Friday.

“At the moment, the plan remains for the United States and Iran, as well as negotiators from Pakistan and Qatar and other countries involved, to meet tomorrow in Burgenstock for the first talks on the implementation of the agreement,” said the Swiss Foreign Ministry in a statement.

The announcement lifted a veil of uncertainty hanging over the meeting at the luxury Burgenstock hotel near Lucerne in central Switzerland, which was first announced on Tuesday.

At the time, it was billed as a signing ceremony for the memorandum of understanding, but the signing went ahead unexpectedly, with President Trump putting down his signature Wednesday at a candlelit dinner outside Paris, as Iranian President Masoud Pezeshkian signed from afar.

The Israeli military said on Thursday that troops deployed to southern Lebanon would remain there, and would “continue to eliminate threats” and strengthen defenses in the area.

In a statement, the Israel Defense Forces said the troops would remain in the “security zone” – an area that straddles Lebanon's southern border with Israel and extends about six kilometers into the country.

“IDF soldiers have been placed in a designated operational area in southern Lebanon, and will continue to remove threats and strengthen the defense of the citizens of northern Israel,” the Israeli military said.

Iran's foreign minister earlier this week said that if Israeli troops remain in Lebanon, it will be considered a violation of the US-Iran agreement, clearly calling for “an immediate and permanent end to military operations on all sides, including in Lebanon.”

At least 10 commercial vessels were tracked passing through the Strait of Hormuz on Thursday morning, while another six were seen heading in the same direction to exit the Persian Gulf.

A significant increase in traffic, but still well below the pre-war average of about 135 ships a day plying the vital waterway, the only route into and out of the Gulf.

Among the vessels is the French-flagged liquefied natural gas (LNG) carrier Mraikh, operated by QatarEnergy. A ship carrying cars belonging to the Italian company Grimaldi Group was also crossing, months after leaving its cargo in Persian Gulf ports. Both ships were among hundreds stranded in the Persian Gulf since the war began, 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 crews, a tactic used by sailors at the beginning of the conflict when Iran said it would target ships linked to the US and Israel.

Several of the condemned Iranian tankers that crossed the U.S. naval blockade earlier in the week were en route to Iranian ports on Wednesday morning.

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

The agreement between the US and Iran calls for a “permanent end to military operations in all sectors, including in Lebanon.”

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

A senior Israeli official told Reuters on Thursday that Israel is “conducting tough negotiations” with the US regarding the deployment of its troops to southern Lebanon.

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

The Israeli army announced on Thursday that its soldiers were killed in the battle in southern Lebanon yesterday in an incident that also injured seven soldiers.

Master Sgt. Alexander Filin, 29, “fell in battle,” the military said in a brief statement, adding that an officer, a reserve officer and a reservist were moderately injured.

A non-combat officer, two reservists and a female reservist were slightly injured, the army added.

The United States and Iran signed an agreement on Wednesday aimed at ending the war in the Middle East, with hostilities on all sides, including Lebanon.

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

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

The Israeli side has seen 31 soldiers and one contractor out of action since March 2.

The US-Iran memorandum of understanding will take effect “as soon as possible” after the presidents of both countries have signed it, said Pakistan's Prime Minister Shebhaz Sharif, who helped mediate talks between the two sides.

Sharif also wrote in X that “as a first step, the Islamic Republic of Iran will immediately open the Strait of Hormuz and the United States of America will immediately remove the shipping embargo.”

“The signing of this agreement at the highest level of the governments involved shows the commitment of both sides to resolve the conflicts,” he said.

President Trump and Iranian President Masoud Pezeshkian signed a memorandum of understanding on Wednesday, a US official told CBS News. Mr. Trump later told reporters that he had signed the Treaty of Versailles when he participated in welcoming 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.