Saudi Arabia indicated a new willingness to support the U.S. search for military facilities in the Persian Gulf region as a result of the threat posed by the Soviet invasion of Afghanistan, members of national security adviser Zbigniew Brzezinski's delegation said today.

Briefing correspondents after two days of talks here with top Saudi officials, members of the U.S. delegation said they detected a change in the Saudi attitude in the year since Brzezinski and Deputy Secretary of State Warren Christopher last visited here.

The Saudis are still reluctant to allow U.S. military use of facilities on their territory, a delegation member said, but they welcome a stronger American military presence in the Middle East and recognize that it requires the use of additional facilities.

"They are prepared to cooperate in that endeavor," a delegation official said. "They're prepared to be more cooperative both inside their country and outside."

The U.S. officials said they did not specially ask the Saudis to allow American use of their military facilities, one of the touchiest points in the often clouded U.S.-Saudi relationship. The Saudis are very sensitive to charges by Islamic and nonaligned nations that they are close to becoming an American client state.

Nonetheless, it appeared after today's talks that Saudi Arabia now is favorably disposed to U.S. facilities in the region, although it is not going to advertise the idea and may even criticize it occasionally.

The United States has publicly sought the use of military facilities in Oman, located at the strategic neck of the Persian Gulf, Somalia, on the Horn of Africa, and Kenya. The Saudis could be especially helpful in persuading Oman and Somalia, both Islamic nations, to go along with the American request.

Brzezinski and Christopher met for two hours last night with Crown Prince Fahd following a 90-minute working lunch with Prince Saud, the foreign minister. Before leaving here this afternoon, the two U.S. diplomats met again with Prince Saud for another 90 minutes.

Officials with the U.S. delegation characterized the talks as "very constructive, very concrete and very positive."

Those characterizations stood in sharp contrast to the visit Brzezinski and Christopher paid to Saudi Arabia last March, shortly after the Egyptain-Israeli peace treaty was signed. Observers noted a cool response here then as Brezinski tried to sell the Saudis on the value of the peace treaty.

This time, however, U.S. officials took a decidedly optimistic tone on the nature of the talks. One said he was impressed by the Saudis' willingness to discuss in detail concrete matters of common concern.

These included ways of dealing with the pro-Soviet troops on its western borders.

Members of the U.S. delegation said the two sides also discussed the hostage situation in Iran with the Saudis. The U.S. side indicated that once the 50 Americans held in Tehran are freed, the United States is prepared to help Iran. Delegation members said this referred to legitimate Iranian security needs, particularly in relation to a threat along their northern border with Afghanistan. "They need things that we have and no one else can provide," said a delegation member.