Because the United States has in the past refused to sell the weapons to Qatar and did not supply them directly to Qatar, the statement said, the missiles ''must have been obtained illegally.'' The United States is seeking information from Qatar, it added. There was no reaction from Qatar. The United States has agreed to sell Stinger missiles to Bahrain, but these have not been delivered and will be strictly monitored to insure that they are not resold.

With few exceptions, the United States has refused foreign requests to buy the missiles, including requests by other Arab nations in the Persian Gulf region. Bahrain was sold 70 missiles to help it defend its territory against potential Iranian attack. The United States has a small military installation at Bahrain, which provides logistical support for United States Navy operations in the Persian Gulf.

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For years, Iran has possessed less capable, Soviet-made portable anti-aircraft missiles, known as SAM-7's. These operate on the same principle as the Stinger, by homing in on the heat of aircraft engine exhausts. U.S. Recovers Soviet Missiles

Two of the Soviet weapons were recovered last week by the United States Navy from an abandoned Iranian gunboat that was drifting in the Persian Gulf, according to Pentagon officials.

Iran has been known to possess a small number of Stingers. Last fall, equipment used to launch the missile was found on an Iranian boat that American forces captured in the Persian Gulf after it fired on American helicopters patrolling shipping lanes. Later, a Stinger missile was retrieved from an Iranian boat that was sunk in the episode.

Intelligence officials said at the time that the Iranians captured a small number of the missiles from a convoy of Afghan rebels near the border between Iran and Afghanistan. Iran is not known to have used the weapons.

The Los Angeles Times, quoting unidentified officials, said Qatar might have bought the weapons from Iran after Iranian forces were unable to make them work. One of the officials suggested that the weapons sold to Qatar were incomplete and militarily useless.

Qatar is a member of the Gulf Cooperation Council, which has urged strong action against Iran to enforce a cease-fire order in the war with Iraq. But Qatar's relations with Iran are not as tense as those of Saudi Arabia and Kuwait, which have been openly hostile to Iran.