WASHINGTON (AP) _ The Pentagon, determined to prevent bullet-proof flak jackets from being shipped to Syria, paid $11.8 million last year to buy the jackets from a West German firm that had been authorized by the Commerce Department to make them for Syria, a spokesman confirmed Thursday.

Michael I. Burch, the spokesman, said the Defense Department was unaware in 1983 of the Commerce Department's decision to authorize the Valentine Mehler concern of Fulda, West Germany, to re-export to Syria bullet-proof garments made of Kevlar purchased in the United States.

When the Pentagon learned of the export license's issuance, it embarked on a ''damage-limiting operation to keep an important item like this from ending up in the wrong hands,'' Burch told reporters.

That resulted in negotiations with the Mehler company that ended in November 1984 with the Pentagon agreeing to pay $11.8 million for 11,000 protective vests and arm and leg guards the firm had already made.

Burch acknowledged the Pentagon had so far been unable to unload the vests and limb guards, which it didn't need in the first place. But he said he was confident they would soon be transferred to other federal agencies that could use them.

''We currently have the flak jacks and plans are being made to distribute them to various government agencies,'' Burch said. ''But those plans are not yet complete.''

The original contract between Syria and Mehler called for the company to buy $10 million worth of Kevlar in the United States and then to weave the material into 63,000 garments for the Syrian Ministry of Defense.

The Commerce Department approved the transaction and re-export plan in 1983, when the United States was trying to improve relations with Syria, in what it described as a routine action that was not precluded by export limits on weapons.

''It wasn't until the contract was let and the manufacturer was liable for delivery and the manufacturer had bought some material to manufacture the vests that we became aware of it,'' Burch said.

Both the Pentagon and White House then objected, expressing concern that Syria might have supplied training and materiel to Islamic terrorists for the October 1983 attack on the U.S. Marine barracks in Beirut. The Commerce Department then rescinded Mehler's license in December 1983, but by then the first shipments of Kevlar had been delivered to the firm.

The company had already produced 11,000 garments from those first shipments of Kevlar and the Pentagon was determined that not even those vests and limb guards be shipped to Syria, Burch said in confirming a Washington Post story.

''The end result is that the Department of Defense paid for these items out of our budget in order to keep them from falling into the wrong hands,'' he said.

Asked if such a mix-up between the two department could occur today, Burch responded: ''We think that we have tighter control now. All agencies within the government are aware of our policies and concerns and we hope that there would not be a repeat of this type of incident.''