He told reporters outside the White House on Saturday.
They want to make an agreement where they open the strait immediately because they have so much to lose, he says of Iran.
Trump thus confirms information from sources to The Wall Street Journal.
The president is reported to have said privately that he expects strikes against Iran to resume after the US midterm elections in November. But according to the sources, Trump's view of the war could shift quickly and also be affected by how the midterm elections end.
According to Iran's proposal for a seven-day ceasefire, the Strait of Hormuz would have been opened in exchange for, among other things, the US lifting the naval blockade and all sanctions on Iranian oil.
Publicly, Trump has said that after the midterm elections, Iran wants to reach an agreement that dismantles the country's nuclear programme - but behind closed doors, he is doubtful that Iran would agree to his demands, according to the sources.
Both Iranian President Masoud Pezeshkian and Foreign Minister Abbas Araghchi have been in New York in recent days in connection with the opening of the UN General Assembly.
The White House said on Friday that US officials had positive and constructive talks with mediators about the conflict. Earlier this week, Iran held hours-long indirect talks with the US.
