The Gulf Cooperation Council last year ruled the United Arab Emirates has ownership of the islands of Greater and Lesser Tunb and Abu Musa.
Emirati Foreign Minister Abdullah bin Zayed al-Nahyan told the General Assembly that Iran needs to either enter into "serious" negotiations over the status of the islands or face the international courts.
"The (United Arab Emirates) demands of the Islamic Republic of Iran to enter into serious and direct negotiations between the two countries or to refer the issue to the International Court of Justice in the light of its continuous illegal occupation of the three islands, which are an integral part of the territorial sovereignty of the United Arab Emirates," he said.
Iran denied any wrongdoing in the claims of the tiny Persian Gulf islands.
Iran recalled its ambassador to Iraq briefly in 2008 in protest of Baghdad's support for an Emirati move to take ownership of the islands.
The dispute has spilled over to regional affairs as the sparsely populated islands lie close to key oil shipping lanes near the Straits of Hormuz.
Iran isn't a member of the GCC.