It was not clear from Trump's social media post how Iran had communicated that message and no immediate comment from Iran was available.
"Iran has just informed us that they are in a 'State of Collapse.' They want us to 'Open the Hormuz Strait,' as soon as possible, as they try to figure out their leadership situation (Which I believe they will be able to do!)" Trump said in a social media post.
The White House did not immediately return a request for comment on the Truth Social post.
Trump is unhappy with the latest Iranian proposal on resolving the two-month war, a US official told Reuters, dampening hopes for a resolution of the conflict that has disrupted energy supplies, fuelled inflation and killed thousands of people.
Meanwhile, Gulf leaders met in person in Saudi Arabia on Tuesday for the first time since their counties became a front in the Iran war.
A Gulf official said the meeting aimed to craft a response to the thousands of Iranian missile and drone attacks they faced since the US and Israel launched the war on Iran on February 28.
Attacks have subsided since a ceasefire on April 8 although Gulf capitals remain wary of resumed conflict.
Iran's previous nuclear deal with the US and other powers in 2015 sharply curtailed its nuclear program, which it has long maintained is for peaceful civilian purposes.
But that deal fell apart when Trump unilaterally withdrew in his first term in office.
Hopes of reviving peace efforts have receded since Trump last weekend scrapped a visit by his special envoy Steve Witkoff and son-in-law Jared Kushner to mediator Pakistan.
Iranian Foreign Minister Abbas Araqchi shuttled in and out of Islamabad twice during the weekend.
He also visited Oman and on Monday went to Russia, where he met President Vladimir Putin.
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