During the conversation, Johnson reiterated Britain's support for the embattled 2015 Iran nuclear deal known as the Joint Comprehensive Plan of Action, reached between Iran and a coalition including Britain, the United States, Russia, China, France and Germany.
Under the JCPOA, Iran agreed to restrict its civilian nuclear enrichment program in exchange for relief from Western sanctions imposed to deter its steps toward producing a nuclear weapon.
U.S. President Donald Trump pulled out of the agreement in 2018, complaining it failed to address Iran's ballistic missile program and its role in regional wars, reimposing harsh economic sanctions.
Iran in recent months has begun stepping back from its requirements under the deal in response to the reimposed sanctions.
Trump again blasted the JCPOA as a failed effort during a speech Wednesday in the wake of this week's missile attack by Iran on two military bases in Iraq, which came in retaliation for the controversial U.S. killing of top Iranian commander Qassem Soleimani.
During Johnson's conversation with Rouhani, however, the British prime minister "underlined the U.K.'s continued commitment to the JCPOA and to ongoing dialogue to avoid nuclear proliferation and reduce tensions," the statement read.
Pope Francis, meanwhile, also urged a commitment to peace throughout the Middle East and Mediterranean regions in light of the U.S.-Iran tensions.
In his annual address to members of the diplomatic corps assigned to the Vatican on Thursday, Francis said that in view of this week's hostilities, it is crucial "that all the interested parties avoid an escalation of the conflict and keep alive the flame of dialogue and self-restraint, in full respect of international law."