The deal placed restrictions of the sort of nuclear reactor itcould develop, butdid not require it to halt its use of nuclear energy entirely.
Both May andRouhani are among the world leaders attending the UN summit in New York.
Tonight's meeting comes following the jailing ofBritish-Iranian motherNazanin Zaghari-Ratcliffe, who was sentenced to five years in prison in Iran earlier this month.
The 37-year-old mother, from Hampstead in north London, was accused of plotting to overthrow the Iranian regime.
According to her husband,Richard Ratcliffe, shewas sentenced on charges that "remain secret".