"We are not looking for regime change. We are not looking for that at all," the US president said, France 24 reported on Tuesday.
"We'll see what happens. But a lot of progress has been made."
He added, "They can't have a nuclear weapon. They can't be testing ballistic missiles."
Trump did not elaborate on the "progress" made, but US Secretary of State Mike Pompeo said that Iran had said it was prepared to negotiate over its missile program.
Pompeo told a cabinet meeting Tehran had "for the first time" signaled it would discuss the missiles, suggesting this was the result of US economic pressure.
The claim, however, was quickly refuted by Iran's representative to the United Nations.
"Iran's missiles ... are absolutely and under no condition negotiable with anyone or any country, period,” Majid Takht Ravanchi said.
Iranian Foreign Minister Mohammad Javad Zarif has repeatedly said that Tehran would only sit down with the United States if it lifted sanctions it has imposed on Tehran and rejoined the 2015 nuclear deal it abandoned last year.