DUBAI (Reuters) - The United Arab Emirates criticized on Monday a visit by Iranian lawmakers to Gulf islands near the Strait of Hormuz at the center of a territorial dispute between the two countries, who are both trade partners and strategic rivals.

Tension between Shi'ite and Sunni Muslims in a Middle East shaken by two years of political turmoil has sharpened the 42-year-old dispute, complicating an ambivalent relationship in which national pride has vied uneasily with economic pragmatism.

About 40 percent of the world's seaborne oil exports flow through Hormuz. Iran threatened last year to block the Strait as tensions rose with the West over Tehran's disputed nuclear program.

"The Foreign Ministry strongly condemns and categorically rejects a visit by an Iranian parliament delegation to the islands," the UAE state news agency WAM said.

"This visit flagrantly infringes on the sovereignty of the UAE and undermines all exerted efforts towards finding a peaceful resolution for this issue," it said.

The islands, Abu Musa and Greater and Lesser Tunb, are claimed by both countries but have been held by Iran since 1971, shortly before the seven Gulf emirates gained full independence from Britain and formed the UAE, now allied with Washington.

There was no immediate official comment from Iran.

But a report on an Iranian website calling itself the Young Journalists Club said that a delegation of Iranian parliamentarians made a one-day visit to the three islands of Abu Musa, Greater Tunb and Sirri on April 25.

Sirri is not claimed by the UAE. Iran says its sovereignty over the Gulf islands it holds is not negotiable but has called for talks with the UAE to clear up "misunderstandings". A senior UAE foreign ministry official met Iran's UAE ambassador to discussed "important issues of mutual concern", WAM said.

(Reporting by Mahmoud Habboush and Yeganeh Torbati, Editing by William Maclean and Mark Heinrich)

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UAE criticizes Iran lawmakers' visit to disputed islands