Gargash said on Twitter that "the tough strategy announced is a natural outcome of Iranian behaviour" adding that it is the right way for Tehran to understand "the futility of its incursions and expansionism".
"Europe is very, very united in its position on the nuclear accord with Iran, and that will not change".
On Monday Pompeo threatened Iran with "the strongest sanctions in history" if it did not curb its regional influence, accusing Tehran of supporting armed groups in Syria, Lebanon and Yemen.
A senior Iranian military official reportedly argued the U.S.
European banks should "safeguard trade" with Tehran.
Iranian President Rouhani said: "The Iranian nation is not afraid of empty threats and is so much greater than Trump, Pompeo, (John) Bolton and all these people who have gathered in Washington as extremists".
Trump, however, said a "real, comprehensive and lasting solution to the Iran nuclear threat" was being worked on by the U.S. and its allies.
Under the requirements, "Iran has no possible path to a nuclear weapon, ever", Pompeo said.
Trump announced on May 8 that Washington was walking away from the nuclear agreement, which was reached between Iran and the five permanent members of the UN Security Council - the US, Britain, France, Russia and China - plus Germany - in 2015.
Iranian state television said that Trump's decision to withdraw was "illegal, illegitimate and undermines global agreements".
Now that the United States has left the nuclear accord, officially known as the Joint Comprehensive Plan of Action (JCPOA), they can no longer use their stonewalling tactics in the accord's Joint Commission - which regularly meets in Vienna, Zarif said.
Pompeo told a House Foreign Affairs Committee hearing the administration meant to work with "as many partners, friends and allies as possible" to stop what he described as all of Tehran's nuclear and non-nuclear threats.