U.S. President Donald Trump said Monday the United States has studied a proposal for a 45-day ceasefire in the Iran war, a move he called a "very significant step" in the conflict.

"It's a significant proposal, it's a significant step. It's not good enough, but it's a very significant step," Trump told reporters at the White House, adding that intermediaries "are negotiating now."

Iran has rejected a proposed truce in its war with the United States and Israel, state media reported Monday, despite a stark threat by U.S. President Donald Trump to destroy its vital infrastructure.

Iran's Revolutionary Guards said they are completing preparations to enforce new operating conditions in the Strait of Hormuz, which has been all but shut since the war with the United States and Israel began.

U.S.-Israeli strikes killed on Monday the intelligence chief of Iran's Revolutionary Guards, the Guards said.

Iran launched fresh attacks across the Middle East on Monday and threatened "devastating" retaliation, after U.S. President Donald Trump's expletive-laced warning that Tehran must reopen the Strait of Hormuz.

U.S. President Donald Trump on Sunday appeared to extend by 24 hours his deadline for Iran to make a deal to reopen the Strait of Hormuz or face devastating infrastructure attacks.

U.S. President Donald Trump said Sunday he believes there is a "good chance" of making a deal with Iran on Monday, ahead of his deadline for Tehran to reopen the Strait of Hormuz or face heavy bombing.

U.S. President Donald Trump said Sunday that U.S. forces had safely recovered a second airman downed in Iran, calling it "one of the most daring Search and Rescue Operations in U.S. History".

U.S. President Donald Trump said that "many" of Iran's military leaders were killed in a huge strike on the Islamic republic's capital.

Over the last ten days the U.S. and Iran have held indirect negotiations through Pakistan, Egypt and Turkey to try and reach a deal of a ceasefire in return for opening the strait of Hormuz. No significant progress has been achieved so far, U.S. news portal Axios reported on Saturday.