The EU has said it will "spare no effort" to keep the nuclear deal alive, despite the escalating tensions between Washington and Tehran.
After the United States reimposed sanctions on Iran, Tehran started breaching some aspects of the accord and on Sunday announced that it no longer felt compelled to stick to any limit on the number of its centrifuges for making the enriched uranium needed for nuclear power.
Following the meeting, he said that foreign ministers had given him a strong mandate to conduct diplomacy with all sides, including Iran, in order to de-escalate the crisis and search for a political solution.
Tehran responded earlier this week with missile strikes at USA bases and announced it would no longer respect limits set under the 2015 nuclear deal on how many centrifuges it can use to enrich uranium, fuelling fears Iran could quickly start building a nuclear arsenal.
Despite calls from US president Donald Trump to break away from the deal, which is aimed at preventing Iran from getting atomic weapons, the European Union remains committed to the treaty amid an escalation of tensions in the region.
"The use of weapons must stop now to give space for dialogue", she said on Wednesday.
Johnson's spokesperson says that during the phone talks, the prime minister called for an "end to hostilities" and "underlined the UK's continued commitment" to the nuclear deal. "There can not be enough of that".
Tehran's limited strike on two bases - one in the northern Iraqi city in Irbil and the other at Ain al-Asad in western Iraq - appeared to signal that it also wanted to avoid a wider clash with the US.
On Monday, Iran announced that it was scrapping the limit set on uranium enrichment, under the agreement.
It would take longer to build an arsenal and launch system, although Tehran has already developed its own short-range and medium-range ballistic missiles with sufficient range to hit targets in parts of Europe.
A Downing Street spokesman said Johnson held a phone call lasting 20 minutes with Rouhani on Thursday, and reaffirmed United Kingdom support for the worldwide deal with Iran over nuclear capabilities, formally known as the Joint Comprehensive Plan of Action, or JCPOA.
Iran, he said, is getting "hurt very badly" by the sanctions.
Britain, France, Germany, the European Union, China and Russian Federation have remained in the pact, which limited Iran's uranium enrichment program in exchange for an easing of sanctions.
Iran insists its nuclear program is for civilian purposes only, and the JCPOA allows the country to run reactors to generate power.
Mr Raab welcomed US President Donald Trump's call for a diplomatic resolution following Iran's retaliatory missile strikes.
This as Europe looks for ways to guide the United States and Iran away from open conflict, knowing that a miscalculation from either side could leave the bloc facing a war and a serious nuclear proliferation crisis at its doorstep.
Iran is hoping to improve economic ties with European and other nations under the current nuclear deal.