A call for the United States to compete with Soviet influence in South Yemen, opposite the Horn of Africa, received a cool response yesterday from the State Department.

Soviet forces, expelled in November from their naval base at Berbera, in Somalia, are using South Yemen's strategic port of Aden, and its airfield, to help supply Ethiopia with weapons in its expanding war with Somalia. American-armed Saudi Arabia and Iran, in turn have come to the aid of Somalia.

A rare American visitor to South Yemen, Rep. Paul Finley (R-Ill.), just back from a trip to Aden, yesterday urged the Carter administration to resume diplomatic relations with that maarxist-ruled nation to counter the Soviet Union.

"I think it would be a very serious blunder," Finley said in an interview, "if our government fails to move in there."

A State Department official countered that "we just don't feel the situation is conductive at this time."

South Yemen, officially known as the People's Democratic Republic of Yemen, is providing military adviers to Ethiopia with Cuba and the Soviet Union, State Department spokesman Hodding Carter III said yesterday.

There are "roughly 300" South Yemeni in Ethiopia, "in combat areas of the Ogaden and in Eritrea," said Carter, and "we believe that the numbers are increasing."

Militarily, U.S. officials said, the number of South Yemeni advisers is not significant compared to the Cuban and Soviet advisers in Ehiopia, who reportedly total about 3,000. However, the South Yemeni presence is regarded as ideologically important to the Soviet Union. Ethipia was formerly an American client.

South Yemen's prime asset is its port of Aden, developed by Britain, which until 1967 ruled the poor nation on the southern coast of the Arabian peninsula. Its population is 1.7 million.

According to the State Department, for the last five years there have been about 500 to 700 Cuban advisers in South Yemen, half of them training the militia. At present, these sources said, South Yemen also has about 700 to 800 Soviet advisers, 200 to 300 East European advisers and 100 to 200 Chinese.

South Yemen broke diplomatic relations with the United States in 1969. Last fall, the Carter administration set out to resolve relations, but then backed off, on grounds that South Yemen was becoming increasingly radical on Arab-Israeli negotiations and other issues.

Findley, a senior member of the House International Relations Committee, visited South Yemen Jan. 13-15. He said Saudi Arabia, whose lead the United Staes tends to follow in the region, is anxious to make new moves to offset the Soviet presence. He said he saw a Soviet destroyer and two supply ships in the harbor, and "it is common knowledge" that a Soviet drydock has been moved from Berbera to Aden.