The bulk of American infantry power in South Korea will remain here until the very end of the U.S. pullout of ground forces in 1982, according to an agreement worked out by Secretary of Defense Harold Brown and South Korean officials during two days of discussions.

Two bridages of the 2d Infantry Division - 8,000 men plus another 4,000 in support units - will serve as a rearguard covering the withdrawal of most of the 31,000 ground troops now in the country.

Other points the withdrawal and simultaneious buildup of South Korean defenses disclosed in a joint communique issued after the talks and by Brown at a press conference today were:

The American nuclear umbrella will continue to cover this country following the withdrawal of ground forces.

Congress will be asked to approve foreign military sales credits to South Korea totalling an estimated $1.9.

The first 6,000 GIs will go home next year, 25 years after the end of the Korean War.

The United States has agreed "in principle" to sell a number of F-16 jet fighters to Seoul, although it will be several years before production orders can be filled.

Looming over the withdrawal plan is the uncertainly of Congressional reaction to a request for aid funds to a nation under investigation for allegedly bribing American politicians. A senior American officials said he did not know if the withdrawal would continue if the appropriations were refused.

Brown said that while he expected some adjustments following consultation with Congress, he was confident that the program would go forward. A key sentence in the communique stated that measures to build up South Korean defense forces would be implemented "in advance of or in parallel with the withdrawals."

The communique emphasized that the U.S. commitment to the defense of South Korea made in a 1954 treaty is absolutely unchanged. President Carter has stated American's undiminished determination "to provide prompt and effective support" if South Korea is attacked.

Brown told the press conference: "So long as an American security commitment exists, no one should have any doubts about our willingness, our intention of honoring it."

U.S. air power, which is to be reinforced and stationed indefinitely in South Korea together with other sea, land and air forces in the area, were a clear demonstration of U.S. determinatio, Brown said. The withdrawal, he added, was consistent with America's firm intention "to continue as a major power in the Western Pacific and East Asia."

Washington will assist the South Korean military buildup with the free transfer of U.S. equipment now in the country and with loans to buy other weapons, including the F-16.

American officials concede that implications of the scheduled withdrawal have caused concern among South Korea officials. One senior U.S. official said President Park Chung Hee raised several questions following an earlier briefing on the pullout plan.

Brown brought Carter's replies to Seoul and the South Korean leader was said to be reasonably satisfied.

The lengthy and detailed consultations between the two governments that culminated in the past two days of talks involved an effort to restore Seoul's shaken confidence in U.S. intentions.

U.S. Ambassador Richard L. Sneider said today: "We're not pulling out of this place and we're not fool-hardy and we're not about to commit hara-kiri here. It's obviously as much in our interest as it is in the Koreans' interest to do the job the right way."

American diplomats say they believe they have been successful in convincing the South Koreans that the withdrawal of U.S. troops does not lessen the American commitment.

The agreements to keep the bulk of the 2d Division here until the very end and to sell the F-16 to South Korea are major concessions in what had been the Carter administration's original plans.

It remains unclear whether the United States is prepared to return ground troops here should war break out. An American official said the issue was not discussed with the South Koreans. Yet, the stated readiness to honor the defense treaty commitment and the formation of a joint command to develop redeployment plans seems to imply that the United States stands ready to return infantry troops.

In discussing the continued extension of the U.S. nuclear umbrella here, Brown said he thought it would be a mistake for a county capable of defending itself by conventional means to rely on nuclear weaponry. The U.S. government does not contemplate their potential use lightly, he said. "They are an extreme measure . . . which is very unlikely to promote the survival of those who use them or those on whom they are used."

Questions raised by South Korean reporters at the press conference reflected continuing skepticism here about U.S. intentions.

Brown was asked why the United States was not withdrawing troops from Western Europe. He cited the vast differences between the military strength of North Korea compared with that of the Soviet Union and its Warsaw Pact allies.

Asked what led to the pullout decision, Brown noted South Korea's growing economic and military strength and said that there were clear indications that neither the Soviet Union nor China were prepared to encourage North Korea in any military adventure.

The withdrawal offered an opportunity to stabilize Northeast Asia, he said, adding: "It will be a more stable situation if the balance of military power does not depend . . . on the presence of U.S. ground forces."