The sanctions are meant to hinder Tehran's acquisition of US currency; its precious metals trade; bank transactions denominated in the Iranian rial; activities related to Iran's sovereign debt; and the country's automotive sector.
"It's a disloyal attitude towards the honest position of Iran and the blood of the martyrs this country has spilt to defend the land of Iraq" against extremists, said Moujtaba al-Hussein.
Johnson wrote in his article that British businesses should cut all trade ties with Iran and help the USA form a "united front".
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.
Iran has cancelled a visit by Iraq's prime minister after he said that while he was opposed to renewed U.S. sanctions on Tehran he had no choice but to abide by them, an Iraqi official said.
Trump pulled out of the deal in May and last week began reinstating economic sanctions against Iran that were eased in exchange for concessions on Iran's nuclear program.
Trump announced on May 8 that he would abandon the Joint Comprehensive Plan of Action (JCPOA), a landmark nuclear deal between Iran and six world powers - the United States, the UK, France, Russia, China and Germany. "It is time to move on from the flawed 2015 deal", he said.
The administration is poised to impose a second wave of sanctions in November.
The US pullout has been met with disbelief by European allies, who issued a statement on Monday committing to the 2015 deal and encouraged investors to maintain business ties with Iran.
Asked about Johnson's article, the British foreign office pointed to comments from Middle East minister Alistair Burt, who last week ruled out Britain going along with the United States.
May's position is likely to become even more awkward in the coming days as she's forced to choose between European leaders, whose support she needs for a favorable Brexit deal or a USA leader determined to secure EU compliance with reimposed sanctions on Iran, fear British officials.