"Taking into account that the British side insists that its servicemen were fulfilling their UN Security Council mandate, we believe the UN Secretariat should prepare an independent report on the incident shortly," the ministry said following a meeting between Deputy Foreign Minister Alexander Yakovenko and British Ambassador to Russia Tony Brenton.
Iran detained the British sailors in the Gulf last Friday for allegedly violating its maritime border with Iraq. Britain insists its servicemen were captured in Iraqi waters when returning to the HMS Cornwall after patrolling oil platforms under a UN mandate.
Yakovenko said the incident called for a thorough investigation, and Brenton said his country would promptly provide the UN with relevant information, the ministry said. It added that the diplomats had agreed to continue discussing the matter.
London earlier cited satellite data, saying the sailors were 1.7 nautical miles away from Iraq's maritime border with Iran.
Western agencies reported Friday that the European Union had demanded the immediate release of the seamen at an informal meeting of its foreign ministers, which was dominated by discussions of pressing international problems in Germany's Bremen Friday.
London froze official bilateral contacts, suspended the issuance of visas to Iranian officials and referred the situation to the UN Security Council Wednesday. The UN has expressed "grave concern" over the sailors' capture.