To add details

DUBAI, June 23 (Reuters) - U.S. President Donald Trump said on Tuesday that Iran had agreed to nuclear inspections "indefinitely," but Tehran denied this, adding that released Iranian assets would be used to buy humanitarian supplies from the United States.

The United States granted Iran a 60-day reprieve from sanctions starting Monday, following the first round of talks under a preliminary agreement signed last week to end a war that lasted more than three months.

U.S. Vice President J.D. Vance said that talks with Iranian officials in Switzerland laid a good foundation for a final agreement and that Iran had agreed to the return of International Atomic Energy Agency inspectors to the country.

But Iran denied that it had begun discussions about its nuclear program or agreed to invite inspectors from the International Atomic Energy Agency to return.

Iran: We will decide what to do with our assets.

Iranian Foreign Ministry spokesman Ismail Baghaei said on Tuesday that Iranian officials had not held any meeting with International Atomic Energy Agency Director General Rafael Grossi in Switzerland, and that they had no plans to allow the agency to conduct inspections of damaged Iranian nuclear facilities.

Trump responded on Tuesday to what he called "false protests and statements" from Iran.

Trump said in a post on Truth Social, "Iran has fully and finally agreed to the highest level of nuclear inspections for a long time to come (indefinitely)."

He also stated that any Iranian assets released under the agreement would be placed in an escrow account and used to purchase food and medical supplies from the United States, "including corn, wheat, and soybeans from our great American farmers."

Iran’s ambassador to the United Nations, Ali Bahreini, had earlier today denied that any such agreement had been reached.

He told reporters, "Iran is the only country that decides what to do with its assets that will be released, and therefore I reject any claim that any other country has any role in influencing these decisions or those procedures."

* Roadmap for talks

These conflicting statements highlighted the uncertainty surrounding negotiations aimed at ending a war that has turned the Middle East upside down.

The mediators, Pakistan and Qatar, said that the two sides agreed during talks held at the Swiss mountain resort of Bürgenstock on a roadmap to reach a final agreement within 60 days, in an attempt to build on the interim agreement they signed last week after a war that lasted more than three months.

The two sides agreed on a mechanism to end the fighting between Washington's ally Israel and the Iranian-backed Lebanese group Hezbollah, and opened a line of communication to help ensure the safe passage of commercial ships through the Strait of Hormuz, a vital waterway for global oil supplies that Tehran closed during the war.

In the first of several steps expected under the agreement to provide economic support to Iran, the US Treasury Department announced a waiver of sanctions until August 21, allowing Tehran to sell oil and related products and receive payments for them.

Bahraini said that "good progress" had been made in the talks, and that two working groups would be formed in the coming days to focus on the issues of lifting sanctions and Iranian nuclear activities.

He told reporters that five items of the preliminary agreement must be fully implemented before negotiations can begin on the nuclear issue and any role for the International Atomic Energy Agency.

Conflict in Lebanon

The diplomat also said that Lebanon is "undoubtedly" included in the interim agreement between the United States and Iran, adding that the agreement stipulates the withdrawal of Israeli forces from Lebanon.

The ceasefire in southern Lebanon has largely held since Sunday, but Lebanese civil defense and state media reported that Israeli fire killed two people there on Tuesday. Hezbollah said the attack violated the ceasefire.

Israel said it would maintain a security zone in southern Lebanon and would continue to act to "neutralize" threats against Israeli soldiers and civilians.

Israel and Lebanon are scheduled to begin a new round of talks in Washington today. Israeli attacks on Hezbollah have killed thousands and displaced millions.

Oil tanker traffic through the Strait of Hormuz began to increase yesterday, but Iran and Oman hinted in a joint statement at the possibility of imposing fees for the use of the strait, whose closure has led to higher oil prices and global inflation.

Oman and Iran said a joint working group would seek to reach an agreement on managing navigation in the Strait, the services provided, and associated costs. They added that any arrangement must respect their sovereignty and sovereign rights.

* A political burden on Trump

Oil prices have fallen since the interim agreement was reached. Crude prices continued to decline on Tuesday after closing down 3 percent at settlement on Monday.

The war with Iran has become a domestic political burden for Trump and his fellow Republicans in Congress as the midterm elections approach in November .

Public opinion polls show that Americans are deeply frustrated by rising gasoline prices since the war began. Trump also faces pressure from Republicans who say Iran's nuclear program must be stopped entirely.

Iran restricted inspections by the International Atomic Energy Agency (IAEA) after the United States and Israel launched their first round of airstrikes last year, and suspended them entirely when war broke out in February. Iran maintains that its nuclear program is peaceful.