The UN nuclear watchdog has confirmed that Iran earlier this month violated the 2015, accord, and Iran's supreme leader on Tuesday said Tehran would keep removing restraints on its nuclear activity in the deal.
In her last major speech before stepping down next week, May said the nuclear deal must be protected "whatever its challenges".
"Whether we like it or not a compromise deal remains the best way to get the outcome we all still ultimately seek - to prevent Iran from acquiring a nuclear weapon, and to preserve the stability of the region," May said.