British Prime Minister Theresa May held talks with Turkish president Recep Tayyip Erdogan on Tuesday, which included Cyprus.
Other issues were Bashar Assad’s regime in Syria and the security situation in Somalia, Downing Street said.
May “underlined the importance of our strong security partnership” and expressed her desire to “deepen co-operation on a range of issues” during the phone call.
A Number 10 spokesman said: “The Prime Minister and President Erdogan discussed the ongoing Cyprus settlement talks and the Prime Minister reiterated that while there remains an opportunity for an historic agreement to be reached, all parties need to be prepared to take bold steps.
“She added that the UK stands ready to play a role in seeking a solution.”