The US-E3 talks dominated Trump's conversation with Prime Minister Benjamin Netanyahu at the White House last week.
"President Trump has called on the Congress and our European allies to enact real and lasting restraints on Iran's nuclear and ballistic missile ambitions".
The US president added that for those reasons, he has "determined it is necessary to continue the national emergency declared with respect to Iran and to maintain in force comprehensive sanctions against Iran to respond to this threat".
If Trump opts to reimpose US sanctions on Iran after May 12, European Union officials have warned that Brussels might try to block the American measures and protect European companies investing in the Iranian market.
Israeli officials said that they believe Trump is serious in his threat to withdraw from the deal by mid- May unless these three European governments - the "E3" - demonstrate their willingness to renegotiate on these points.
The crux of the July 2015 pact between Iran and six major powers - Britain, China, France, Germany, Russia and the United States - was that Iran would restrict its nuclear program in return for relief from sanctions that have crippled its economy.
In a January 13 cable, the State Department sketched out a path under which the three European allies would simply commit to try to improve the deal over time in return for Trump keeping the pact alive by renewing sanctions relief in May. But analysts said European banks and other firms are already reluctant to do business in Iran due to the threat of a possible "snap-back" of USA sanctions and don't want to lose their access to the vast American market.
Iran, of course, doesn't have a nuclear weapons program, and didn't have such a program for years before the deal was made. A USA withdrawal could wreck the agreement, scaring off European investment that Iran saw as a key reward for agreeing to limit its uranium enrichment and other nuclear work.
Other European officials and former US officials said Pompeo's rise, if he is confirmed as secretary of state by the Senate, might have a more ambiguous effect on the negotiations and that, in any case, Trump's views are paramount.
Iranian Deputy Foreign Minister Abbas Araqchi said during a speech at the Chatham House think tank in London that Tehran can not remain in the nuclear deal, known as the Joint Comprehensive Plan of Action, if it can not benefit from it.
In the past two months, the four nations have held two talks.
Army General Joseph Votel, commander of the U.S. Central Command, testifies before the Senate Armed Services Committee on Capitol Hill in Washington, March 13, 2018.