Trump also said that he did not want to meet with Iran's Supreme Leader Mojtaba Khamenei.
One of Trump's central objectives in launching military strikes against Iran was to ensure Tehran does not develop a nuclear weapon.
Netanyahu said he is sceptical of a deal but it must include enriched material leaving Iran.
A Syrian source familiar with the matter said the visit was expected to take place within the next two weeks.
The snapback mechanism can be used to restore U.N. sanctions before the U.N. Security Council resolution enshrining the deal expires on October 18.
Muttaqi emphasized the Islamic Emirate’s firm opposition to any foreign military presence in the country.
The Israeli and U.S. strikes targeted a nuclear programme which Western countries have long said was aimed at building an atomic weapon.