Trump's deadline for an "acceptable" deal - one that includes the free flow of energy through the Gulf - is set for 20:00, Washington DC time on Tuesday (00:00 GMT Wednesday).BBC reported.
Speaking at the White House, Trump said that he believed "reasonable" leaders in Iran were negotiating in "good faith", but the outcome remained uncertain.
Iran has rejected proposals for a temporary ceasefire, instead calling for a permanent end to the conflict and the lifting of sanctions.
Trump's news conference held alongside General Dan Caine, the chairman of the Joint Chiefs of Staff and defence secretary Pete Hegseth comes days after US forces successfully recovered two crew members of an F-15 fighter jet that was downed in southern Iran.
