ISLAMABAD, Pakistan (AP) _ Afghanistan's Soviet-backed government said Thursday it has purchased sophiticated anti-aircraft missiles from guerrillas fighting against it, Radio Kabul said.

There was no immediate guerrilla comment on the report.

Afghanistan's official radio, monitored in Islamabad, said Kabul bought one U.S. heat-seeking Stinger missile and a British radar-guided Blowpipe rocket, ''and paid the price on the accepted standard.''

It did not say when or where the purchase took place, or specify the price.

In Washington, a senior State Department official, who spoke on condition of anonymity, said he had not heard of such a sale, and called it ''highly doubtful.''

But David Isby, military specialist of the Committee for Free Afghanistan, one of several private U.S. groups supporting the rebel cause, said he had heard that a guerrilla recently had defected and brought government authorities a Stinger.

The governing People's Democratic Party of Afghanistan last month offered to buy arms from Moslem insurgents in an effort to split the opposition.

The guerrillas, known as Mujahedeen, have made a major dent in the Soviet- Afghan air advantage since they acquired the advanced surface-to-air missiles in the fall of 1986.

Party leader Najib, who also is Afghanistan's president and goes by a single name, has been promoting a unilateral cease-fire. He has invited the guerrillas to join in a coalition to clear the way for the complete withdrawal of Soviet troops.

The Moslem resistance, based in neighboring Pakistan, has rejected any power-sharing deal with the communists, insisting on an Islamic government free of foreign involvement.

Kabul's pro-Moscow government seized power in a bloody 1978 coup and Soviet troops rushed in to back it up 18 months later. About 115,000 Soviet troops remain.

Andrew Eiva, chairman of the Federation for American Afghan Action, another private U.S. group backing the rebels, estimated that the guerrillas had received more than 1,000 Stingers the past year.

Last month, Secretary of Defense Caspar W. Weinberger dismissed speculation that Afghan rebels had sold U.S.-supplied Stinger missiles to Iran. Weinberger said Iran may have seized such missiles from the guerillas when a truck convoy broke down near the Iran-Afghanistan border.