"Iran really wants to make a deal, and it will be a good one for the U.S.A. and those that are with us," Trump posted on Truth Social.

Iran warned on Sunday the United States was not to be trusted, saying Tehran would not agree to any deal with Washington unless it fully secured Iranian rights.

Iran's chief negotiator Mohammad Bagher Ghalibaf's remarks came as reports emerged that President Trump had sent a tougher peace proposal back to Iran, and underlined the rift that the parties still need to close.

Any tweaks to the draft could further delay an agreement to formally end the Middle East war and reopen the Strait of Hormuz after weeks of fraught negotiations marked by sharp rhetoric and occasional flare-ups of violence.

Iran was already in talks with the United States about the fate of its nuclear programme in February when the US and Israel launched air and missile strikes that wiped out much of the Islamic republic's senior leadership.

And, while Tehran has long insisted that its nuclear programme is for purely civilian ends, the United States and its Western allies suspect it aims to develop a weapon.

The New York Times and Axios reported on Saturday that Trump had sent back a "tougher" new framework to be considered by Iran, though details remain unclear.

Trump has said his priorities include stopping Iran from developing any nuclear weapon and reopening the Hormuz shipping lane, which Iran has blockaded since the war began.

"The one guarantee that I have to have is that there will be no nuclear weapons. They've agreed to that, and it was very interesting," he told his daughter-in-law Lara Trump in an interview on her Fox News show.

Tehran, however, has previously cast doubt on Trump's assertions and the sides remain far apart on key issues.

"We will not approve any agreement until we are certain that the rights of the Iranian people have been upheld," Ghalibaf said in a video broadcast on state television.

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