In May, Trump faces a bigger deadline on whether to waive sanctions on Tehran; and, given his very public displeasure with the nuclear agreement, the prospects do not look good.
Observers believe the tensions between the two countries are driven largely by domestic US politics.
Trump has recently replaced members of his administration that advocated the nuclear deal with hardliners who are calling for scrapping it.
Iran, in turn, has indicated that it would not feel bound by the deal at all if the US walks away from it.
Al Jazeera's John Hendren reports from Washington.