The General Convention of the Episcopal Church today chose Bishop Edmond Lee Browning of Hawaii, a liberal who has supported civil rights, nuclear disarmament and women priests, as the church's next presiding bishop.

The House of Bishops chose Browning, 56, on the fourth ballot, passing over Bishops John T. Walker of Washington, William Frey of Denver and Furman Stough of Burmingham. The four were nominated last spring by a special committee of priests, lay persons and bishops.

Decked with a thick lei of red carnations, Browning told cheering convention-goers after his election that he "hoped to offer a ministry of servanthood" for his 12-year term as chief executive officer of the 2.8 million-member church.

"I believe I am here because of the will of God and because of the prayer of the church," said the new leader, accompanied by his wife, Patricia, and one of their five children.

At a subsequent news conference, he discussed a range of issues.

Of President Reagan's sanctions against South Africa, he said, "I thought he could have done much more."

Describing himself as a "personal friend" of South African Bishop Desmond Tutu, Browning pledged that the Episcopal Church would continue in its "very supportive role for the black majority in South Africa."

On ordination of avowed homosexuals to the priesthood, banned by the church, he said, "I do not believe we should put anybody down. I don't believe you should legislate against people." He said he favors letting dioceses decide on individuals' fitness for ordination.

In 1979, Browning joined more than a dozen other bishops in signing a "conscience statement" challenging the church's stance on ordaining homosexuals.

Of ordaining women, he said, "I am tremendously committed to enhancing the ministry of women," beginning with appointment of them to his new staff. He said that six women priests serve in Hawaii and that four have charge of parishes.

Browning also praised church efforts to develop improved relations with other religious groups, particularly Roman Catholics and Lutherans.

In his nine years in Hawaii, he has led the relatively small Episcopal Church into several cooperative programs with other religious groups, including Buddhists.

Some observers said Browning's unusually diverse career in the church helped him win the election.

Born in Corpus Christi, Tex., he was educated at the Episcopal-related University of the South. He was ordained in 1955, served in Texas for four years, then went to Okinawa as a missionary. He was ordained Missionary Bishop of Okinawa in 1968.

In 1971, he was appointed bishop-in-charge of Episcopal congregations in Europe, mostly near military installations. One of his tasks involved counseling Vietnam-era draft resisters and deserters, particularly in Sweden.

From 1974 to 1976, he was on the church's national staff in New York as executive for world missions, a post that gave him high visibility. He has been in Hawaii since then, serving about 10,000 Episcopalians.

"I've probably had more jobs than most bishops," he said today, adding that "when I've gone into something new, I've tried to listen to where the church was and what the job called for."

He said he would apply the same philosophy to his new job.

While the bishops were sequestered for balloting at St. Michael's Church several miles from the Convention Center, the other legislative body, the House of Deputies, continued with business.

At 10:45 a.m., the Rev. James Foltz, assistant secretary of the House of Bishops, stepped to the lectern and said solemnly, "By the grace of God, the House of Bishops has elected a presiding bishop."

Anxious deputies had to wait another 10 minutes until the Committee on Consecration of Bishops formally considered the decision, recommended concurrence and announced Browning's selection.