The nuclear negotiations have been plagued by contradictory, anonymously leaked information coming from Iran, testament to a conflict between the administration of the outgoing President Hassan Rouhani, the relatively moderate cleric who clinched the 2015 deal, and the hardliners now seeking to replace him.
Pompeo and Grossi pledged to stay in close contact on nuclear issues of concern, the statement added.
"The United States fully supports the IAEA's monitoring and verification activities in Iran, and we are alarmed at Iran's lack of adequate cooperation," Pompeo said in a statement.
Amano had overseen a landmark nuclear deal between Iran and six major world powers in 2015 that restricted the Islamic republic's uranium enrichment programme.
Amano has been the director-general of the International Atomic Energy Agency (IAEA) since 2009 and his latest mandate had been due to run until 2021.
The International Atomic Energy Agency had earlier confirmed that Iran had breached the deal's cap on stockpiling of low-enriched uranium.
