The visit by Yukiya Amano, the head of the International Atomic Energy Agency, comes as the US Congress weighs the deal.
Trump's refusal this month to re-certify the agreement has sparked a new war of words between Iran and the United States, fueling growing mistrust and a sense of nationalism among Iranians.
In a statement issued by his office, Rouhani said Iran's adherence to the deal "has been complete and remarkable."
"We should not allow the (nuclear deal), as an important achievement, to be undermined, and we must consolidate this important international commitment with full cooperation." he added.
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Earlier Sunday while at a news conference, Amano said that "as far as nuclear-related commitments are concerned" Iran is implementing the requirements of the deal.
Iran struck the deal with world powers in 2015. It saw Iran limit its enrichment of uranium in exchange for the easing of economic sanctions. The West had put the sanctions in place over fears Iran's nuclear program could be used to build an atomic bomb.
The European Union, Britain and other parties in the deal have all encouraged Trump to keep the accord in place.
However, Trump punted the issue to Congress, instructing lawmakers to toughen the law that governs US participation in the deal and calling on the other parties to the accord to fix a series of deficiencies.
If they can't, Trump said he will likely pull the U.S. out of the deal and reinstate previously lifted US sanctions on Iran's nuclear program, which could be a mortal blow to the agreement.