A joint prayer vigil by American and Soviet church leaders scheduled to begin tomorrow in Geneva is the latest and most dramatic development in a little-known effort to build permanent relationships between the member churches of the World Council of Churches in the United States and the Soviet Union.

The vigil will bring together two high-level delegations, one headed by Bishop Philip R. Cousin, president of the National Council of Churches, and the other headed by Metropolitan Filaret of the Russian Orthodox Church.

Their purpose is to pray jointly for the success of the Geneva summit talks between President Reagan and Premier Mikhail Gorbachev that begin Tuesday. The vigil will continue through the week.

Patriarch Pimen, head of the Russian Orthodox Church, said in a cable to the NCC Governing Board, "We come with you in prayer for saving humanity from the growing threat of nuclear self-destruction, and that our great nations may proceed from confrontation to cooperation."

The Rev. J. Martin Bailey, associate general secretary of the NCC, said, "We are not negotiators. We are not military experts. Our response is to affirm the importance of the summit meeting and to pray for its success."

Although the vigil culminates nearly 30 years of U.S.-Soviet church relations, it is the first time church leaders from the two nations have engaged in a joint action involving their governments, and it is viewed by many observers as a major breakthrough in the relationship.

The delegation from the United States will include several major denominational leaders, as well as Bishop Cousin and the Rev. Arie Brouwer, general secretary of the NCC. The Soviet delegation will include Baptist leaders, Orthodox bishops and possibly representatives of other denominations.

Local prayer vigils in both the United States and the Soviet Union are also scheduled for tomorrow. Some Baptist prayer services in the Soviet Union have been scheduled for the evening in order to coincide with morning worship services in the United States.

Planning for this activity was made possible by the close ties built between church leaders in the two countries over the last several years. The Rev. Bruce Rigdon, a professor at McCormick Theological Seminary in Chicago, has played a major role in developing the relationship, and traveled to Moscow in October to make arrangements for the vigil.

Rigdon also has led large delegations of U.S. church members to the Soviet Union in the last two years. In 1984 a group of 266 Americans visited churches in the Soviet Union, and this summer an 81-member delegation made the same trip.

There also have been several visits to U.S. churches by smaller delegations from the Soviet Union.

The relationship was initiated in 1956 by the Rev. Eugene Carson Blake, a Presbyterian ecumenical leader, and Presbyterians still play a leading role in it.

The contacts have not been without difficulties or criticism. In the early years, when the Soviet church was under intense persecution by the government of Nikita Khruschev, its leaders had to walk an extremely narrow line to keep the contacts alive while not offending the government.

Although government pressure on the churches has decreased, Soviet church leaders are still not free to criticize their government the way U.S. church leaders often criticize theirs. This difference has frequently made serious dialogue between the two groups difficult.

Like the Geneva prayer vigil, most recent U.S.-Soviet church contacts have involved the peace issue. This concern dates back to 1979, when Soviet and U.S. church leaders spent a week together in Geneva hammering out a common position paper on peace called "Choose Life."

The Soviet church's role as a credible voice in the West on behalf of the Soviet people's aspirations for peace has given it new standing with the Soviet government, according to many observers -- a standing it has used to achieve greater freedom for its leaders to travel abroad.

But conservative leaders see this change as a capitulation to Soviet foreign policy. They also emphasize the status of dissident groups that are not allowed to travel outside the country.