Iran took control of the Persian Gulf islands in 1971, after British forces left the region. The islands—the tiny Abu Musa and the nearby Greater and Lesser Tunb—dominate the approach to the Strait of Hormuz, a key waterway through which about one-fifth of the world's oil supply passes.
Iran's Revolutionary Guard and the U.S. Navy patrol the narrow waterway, which Iran had threatened to choke off in retaliation for tougher Western sanctions over its suspect nuclear program.
Since 1992, the UAE has repeatedly claimed the islands and last month at the U.N. General Assembly, it said Iran's "occupation" violates international law.
The news website of Iran's parliament, ICANA.ir, quoted foreign ministry spokesman Ramin Mehmanparast as saying that Iran will either cut or reduce ties with the UAE if it repeats "anti-Iranian, baseless claims."
"If anti-Iranian baseless claims become too much, and downgrading or cutting diplomatic ties becomes the only option to secure national interests, this will be done," Mehmanparast was quoted as saying. "The continuous and repetitive Emirati claims will have a negative impact on various parts of the relationship" with Iran.
The comments mark the first time that Iran has come out threatening to cut ties with the UAE. In the past, Tehran kept saying it was willing to discuss the case in bilateral level—though it never said relinquishing the islands was an option.
Iran is a top trading partner of Dubai, with the Islamic Republic importing annually $10 billion worth of goods on average in recent years.
Mehmanparast also said Iran will have an "immediate reaction against any country that violates Iran's territory" and stressed how the Emirati claims about the islands have been "very provocative for Iranians."
The remarks are part of Iran's harsher stance after the UAE's statement at the General Assembly in September.
In April, a visit by President Mahmoud Ahmadinejad to the islands inflamed the dispute over the territories and prompted an outcry by UAE and its Arab allies. Tehran later vowed to develop the islands through tourism and other industries, though nothing has been reported on that since the visit.
Tehran says the islands have been part of states that existed on the Iranian mainland from antiquity until the British occupied them in early 20th century.
Tehran also maintains that an agreement signed eight years before its 1979 Islamic Revolution between Shah Mohammad Reza Pahlavi and the ruler of one of the UAE's seven emirates, Sharjah, gives it the right to administer Abu Musa and station troops there.
There was no agreement on the other two islands. The UAE insists they belonged to the emirate of Ras al-Khaimah until Iran captured them by force days before the UAE statehood in 1971.