Protestant, Roman Catholic and Eastern Orthodox theologians from four continents have reached what they described as "signigicant points of agreement" on the nature of baptism at a World Council of Churches consultation here.

Baptism is probably by the rite most universally practiced by Christians, almost all of whom consider it the solemn ceremony by which nonmembers formally enter the fold.

But beyond that there is widespread disagreement amont branches of the Christian family about precisely what the rite symbolizes, the way it is to be administered and to whom.

The controversy has divided Christians since the 16th century Protestant Reformation and it has only been in the modern era that different churhces have attempted to reach a consensus on the meaning of their varying doctrines and practices.

Most major Christian branches, including Roman Catholics, Eastern Orthodox, Anglicans, Lutherans, Presbyterians and Reformed churches, allow baptism of either infants or mature persons as the normal rite for Christian initiation. Most also allow the sacrament to be administered by sprinkling water on the initiate, rather than requiring his immersion into a body of water.

Baptists, the Disciples of Christ (Christian Churches), Mennonites and some smaller traditions require "believer's baptism"-usually by total immersion-which is only administered to persons considered mature enough to profess their faith in Jesus Christ.

Although differences over the ceremony continue, there are "signs of bridge-building from both sides," said a statement agreed on by participants in the consultation here.

"Conversations revealed that for some from both groups, the bridge is sufficiently complete to allow mutual recognition of each other's practices," the statement said.

Baptist participants said the report, which will be sent as a recommendation to the World Council of Churches Faith and Order Commission, represented a "breakthrough" because it contained a finding that believers' baptism was the most common baptismal rite referred to in the New Testament.

Roman Catholics, Eastern Orthodox, Anglican, and other participants said the document marked a step forward in ecumenical relations because it also contained a statement accepting the validity of infant baptism and rejecting the practice of allowing baptism to be administered more than once to a Christian believer.

The consultation included theologians from Britain, France, the Soviet Union, Nigeria, West Germany, The Netherlands, Jamaica, Switzerland, Denmark and the United States. It was chaired by Dr. J. Robert Nelson, a United Methodist theologian and longtime leader in ecumenical relations.

"The Louisville consultation indicated that there are grounds for optimism provided always that, as happened at the consultation, existing disagreements are faced openly in frank discussion and are not swept under some ecumenical carpet in the cause of too superficial a consensus," the group said in a communique.