Church leaders from the United States and the Soviet Union will buttress their hopes for a successful Reagan-Gorbachev summit next month with a continuing prayer vigil at the Washington Cathedral, it was announced yesterday.

"We pray constantly for peace," said the Rev. Arie R. Brouwer, general secretary of the National Council of Churches, a sponsor of the vigil. "But on this occasion it is important for the world and especially for our political leaders to know that American and Soviet Christians are praying together."

About a dozen Soviet churchmen from a variety of Christian denominations are expected to join their American counterparts for the vigil, which will begin at 4 p.m. Dec. 6.

Each succeeding day of the three-day summit talks, the prayer vigil will continue with a eucharist service at 7:30 a.m. and continue through 12:30 a.m. Local Washington clerics will join Soviet religious leaders to lead brief prayers on the hour and half-hour, punctuating periods of silent prayer. Both the opening service and the daily prayers are open to the public.

"To underscore that the vigil is a religious rather than a political event, there will be no sermons or addresses," said Cathedral Provost Charles A. Perry.

A great vigil candle, placed in the crossing at the front of the cathedral, will be lighted during the opening prayer service and will continue burning as long as the summit lasts. Each day a smaller candle will be lighted from the vigil fire and will sit on the cathedral altar.

During the 1985 summit, American and Soviet religious leaders gathered in Geneva for a similar vigil.

Leading the group of Soviet churchmen will be Metropolitan Filaret of Minsk and Byelorussia of the Russian Orthodox Church. He will be joined by leaders of Soviet Baptists, Lutheran churches of Latvia and Estonia, the Armenian Apostolic Church and the Roman Catholic Church in Lithuania, a spokesman for the National Council of Churches said.

American participants will include top leaders of mainline Protestant denominations, as well as Washington area church members. Brouwer, who will take part in the opening service, also will address a Dec. 6 rally on behalf of Soviet Jews.