US Ambassador to Britain Woody Johnson criticized Tehran for funding "proxy wars and malign activities" instead of investing in its economy. He used the government's Brexit rhetoric to support his case, saying that "global Britain" should use its "considerable diplomatic power and influence" to force a change of approach.
Mr Johnson even goes over the head of Whitehall and urges British businesses directly to cut ties with Iran.
While ratcheting up pressure on Tehran, the sanctions are worsening rifts between the United States and European allies, and other world powers, which say they remain committed to the nuclear deal, and will not comply with the US sanctions.
FILE - U.S. President Donald Trump holds up a proclamation declaring his intention to withdraw from the JCPOA Iran nuclear agreement after signing it in the Diplomatic Room at the White House in Washington, May 8, 2018. We want to keep our journalism open and accessible and be able to keep providing you with news and analyses from the frontlines of Israel, the Middle East and the Jewish World.
But administration officials say that increasing pressure on Tehran - including through sanctions - aligns with the possibility of talks with Iranian officials.
German business associations have warned that companies are increasingly suffering from Trump's sanctions policies - including those against Iran - as well as the tariffs he is imposing in the escalating trade conflict with China.
"America is turning up the pressure and we want the United Kingdom by our side".
Asked if British companies could expect Britain to stand its ground over deal, a British minister, Alistair Burt, told reporters last week, "They can expect us to do that, yes".
Abadi "will head to Turkey on Tuesday and Iran on Wednesday to discuss economic affairs with the two countries", the official said on condition of anonymity.
In an article in the Sunday Telegraph, he said: "It is time to move on from the flawed 2015 deal".
The U.S. sanctions that began last week prohibit any transactions with Iran involving dollars, gold, precious metals, aluminum, steel, commercial passenger aircraft, shipping and Iranian seaports.
"Only by presenting a united front can we exert the maximum possible pressure on the Iranian regime, and get it to finally change course and put an end to its malign and reckless activities both at home and overseas", said the ambassador.
In Tehran, the foreign ministry was more guarded about a possible visit by Abadi.
While Washington was busy exiting the Iran nuclear deal in early May, Rabat had its own issues with the Islamic Republic.