"In phone call just now, #British PM @David_Cameron welcomed #IranDeal & Iran's constructive role in the negotiations," Rouhani said on Twitter, referring to the talks that led to a historic agreement Tuesday on Iran's nuclear programme.
He added that Cameron had "expressed interest in reopening embassies & expansion of ties in the framework of mutual interest & respect + combating #terrorism in region".
Britain is one of the six world powers -- along with China, France, Germany, Russia and the United States -- that struck the agreement with Iran after a 13-year standoff over its disputed nuclear programme.
The British government said the pair discussed how the "deal would pave the way for stronger relations, and about what that would mean in terms of bilateral relations and our aim to reopen the embassy".
A spokesman said that during their 20-minute phone call, the British premier "welcomed the historic (nuclear) deal and underlined their respective commitments to delivering on it".