Ahmadinejad praised Iran's rich culture during the Wednesday visit to Abu Musa but did not mention the dispute with the UAE, according to the official IRNA news agency.
Iran took control of tiny Abu Musa and the nearby Greater and Lesser Tunb islands in 1971 after British forces left the region. The three islands dominate the approach to the Strait of Hormuz, through which about one-fifth of the world's oil supply passes.
Tehran says the islands have been part of states on the Iranian mainland from antiquity until the early 20th century.
The UAE's Foreign Minister Sheik Abdullah bin Zayed Al Nahyan called the visit a "setback" to efforts at finding at peaceful solution to the dispute.
"This visit will not change the legal status of these islands which are part and parcel of the UAE national soil, " he said.