Meanwhile Downing Street said Theresa May had spoken to the President directly to “reaffirm the UK’s strong commitment to the deal alongside our European partners, saying it was vitally important for regional security”.
Trump has repeatedly denounced the deal – under which Iran agreed to give up nuclear weapons programmes in return for the lifting of economic sanctions – during his election campaign, and he last month denounced it at the United Nations General Assembly as “an embarrassment to the United States”.
However, other signatories including the UK, France and Germany are firmly in favour of keeping the agreement intact.
Failure to certify the so-called Joint Comprehensive Plan of Action (JCPOA) would trigger a 60-day period during which the US Congress would have to decide whether to re-impose sanctions.
Downing Street added: “The PM stressed that it was important that the deal was carefully monitored and properly enforced.
“Mrs May and the President also discussed the need for the UK, US and others to work together to counter destabilising Iranian activity in the region.
“The PM and President agreed that their teams should remain in contact ahead of the decision on recertification.”
Johnson is to meet with Iranian Vice President Dr Ali Akhbar Salehi in London on Wednesday to press for Iran’s continued compliance with the agreement.
Speaking ahead of the meeting with Dr Salehi, the Foreign Secretary said: “The nuclear deal was a crucial agreement that neutralised its nuclear threat. The UK supports the deal and stresses the importance of all parties continuing to uphold their commitments.
“We have made no bones about our deep concern at Iran’s destabilising regional activity, including its ballistic missile programme, but I remain steadfast in my view that the nuclear deal was an historic achievement that has undoubtedly made the world a safer place.
“It was the culmination of 13 years of painstaking diplomacy and has increased security, both in the region and in the UK. It is these security implications that we continue to encourage the US to consider.”
Foreign Office political director Karen Pierce met French, German and EU counterparts on Tuesday evening to discuss the European position on the JCPoA.
Johnson spoke by telephone with Iranian foreign minister Javad Zarif to underline the benefits of the nuclear deal.
The Foreign Secretary also raised concerns about the detention in Iran of all dual UK-Iranian nationals, including Nazanin Zaghari-Ratcliffe who was arrested as she tried to leave Tehran last year with her daughter Gabriella following a holiday.
The charity worker was accused of plotting to topple the regime, which she denies, and later sentenced to five years in prison.
May again lobbied Trump over US tariffs on plane manufacturer Bombardier, which employs more than 4,000 workers in Belfast, stressing “the importance of the jobs provided by the Bombardier factory to the people and economy of Northern Ireland”.
The firm has been hit by a proposed 80% levy on exports following complaints by Boeing that the Canadian-owned company had dumped its C Series jets at “absurdly low” prices.
The Downing Street spokesman added: “The PM also reiterated her condolences to the president in the wake of the terrible shooting in Las Vegas.”