The UAE intends to raise the issue at the Arab League foreign ministers' summit in Cairo on Sunday, he said.
(Click here for a map of the disputed islands)
The accusation came at the meeting of foreign ministers of the six-member Gulf Co-operation Council (GCC) in Jeddah, Saudi Arabia, which is being chaired by the Emirates minister.
The islands, Greater and Lesser Tumb and Abu Musa, have been under full Iranian control since 1992 and the UAE believes Iran has effectively annexed the islands, ignoring the Emirates' claims.
The Saudi Press Agency reported that Mr al-Nuaimi reiterated his call to Iran not to turn down the peace offer aimed at achieving concord and improving relations of friendship and good neighbourliness.
War games
Last week, Iran announced it was preparing to conduct joint naval exercises with the UAE's neighbour and fellow GCC-member, Oman, which has long maintained good relations with Iran despite the islands dispute.