Iran said Thursday it would go to the U.N. to prove that a U.S. spy drone it shot down had entered Iranian airspace, contrary to Washington's claims.

"We'll take this new aggression to #UN & show that the U.S. is lying about international waters," Foreign Minister Mohammad Javad Zarif tweeted, after a U.S. general said the drone was taken down some 34 kilometres (21 miles) off the Iranian coast.

"The US wages #EconomicTerrorism on Iran, has conducted covert action against us & now encroaches on our territory," he wrote.

"We don't seek war, but will zealously defend our skies, land & waters."

With tensions soaring between the two countries following a series of attacks against tankers in the Gulf, the Pentagon confirmed a U.S. surveillance drone had been shot down by Iranian forces.

But it insisted the unmanned aircraft was in international airspace.

The Pentagon released a graphic pinpointing the position of the drone on a map of the Strait of Hormuz, the strategic passage through which some 35 percent of the world's seaborne oil passes.

The downing with an Iranian surface-to-air missile "occurred in the vicinity of established air corridors between Dubai, UAE, and Oman", said Lieutenant General Joseph Guastella, who commands U.S. air forces in the region.

Iran said the "U.S.-made Global Hawk surveillance drone" was hit with a missile "after violating Iranian air space" over the waters of Hormozgan province on the Strait of Hormuz.