ATLANTA, June 10— A new church for the nation's more than three million Presbyterians was created here today, ending a North-South split that dated from the Civil War. 
The Presbyterian Church (U.S.A.) came into being as 12,000 people gathered for a holy communion service that was transmitted by satellite to 24 places around the country. 
Earlier today, 1,000 delegates to the General Assemblies of the United Presbyterian Church in the U.S.A., the Northern wing, with 2.4 million members, and the Presbyterian Church in the United States, the Southern group, with 815,000, voted their denominations out of existence and celebrated the creation of the new church with a parade down Peachtree Street. 3 Million in 12,000 Churches 
The merger, which Presbyterians here speak of carefully as a ''reunion,'' heals a split that occurred in 1861, when Presbyterians in the Confederate States severed ties with churches in the North. 
The new denomination will have almost 3.2 million members in 12,000 churches, making it the fourth-largest Protestant denomination in the United States, after the Southern Baptists, the United Methodists and the National Baptist Convention, a largely black denomination. 
Since the vast majority of the nation's Presbyterians will be in the merged church, the Presbyterian Church (U.S.A.) is expected to exert more influence, as a single entity, in the forums of American Christianity. Several regional units have been operating jointly for years in anticipation of the merger. 
The reunion proposal was presented to the assembly of the Southern church ''with a few tears, but with greater joy,'' by Joyce Bauer of Raleigh, N.C., chairman of the church's committee in charge of the reunion. When the resolution was passed, cheers and applause filled the hall at the Georgia World Congress Center. 
A few minutes later, Lois Bakken of Denver presented the resolution to the assembly of the United Presbyterian Church, with the same results, and the two delegations streamed out of their meeting halls to embrace and join in the parade. 
Leaders of the new church say there will be some difficult days ahead. Their membership is aging faster than the population in general. Long discussions will precede the approval of a new statement of doctrine, or ''Confession of Faith,'' which will try to articulate Presbyterian doctrine in contemporary language. Distribution of Authority 
Committees must determine how much authority is to be given to presbyteries, the regional units of the church, or to synods, which are made up of several presbyteries. 
''I expect to see a church that will place a great deal of reliance on elected policymakers, the people who serve on boards and agencies,'' said Dr. James Andrews, the stated clerk, or chief executive officer, of the Presbyterian Church in the United States, often referred to as the Southern church. 
United Presbyterians, who are mostly in the North, have a reputation for being liberal on most issues while those in the Southern church tend to be more socially conservative. This blend worried some conservatives and liberals, but negotiations appear to have allayed fears that either position would dominate in the new church. 40 Southern Units Withdraw 
About 40 congregations in the Southern church do not approve of the merger and have withdrawn from the denomination. Church officials say they regret the loss but consider it an acceptable price for reunion. 
The Rev. Robert Davidson of New York City, former moderator, or chief elected officer, of the United Presbyterians, said he believed that the withdrawals, mostly by conservative congregations, would result in a church ''generally liberal in its stance.'' 
''Most of our social statements were created together or are very similar,'' he said. ''Recently, for instance, both churches have been very concerned about halting military aid to Central America and about our Government's involvement there.'' 
Dr. William P. Thompson, stated clerk of the United Presbyterians, said ''Our policies on most issues are very similar.'' Under the reunion agreement, policies that differ will be resolved by general assemblies. Problems Ahead in the South 
Five percent of the nation's Presbyterians are black, and many of the blacks are in five presbyteries in the South. There are differing views as to whether those churches should be assigned to presbyteries that are predominantly white or left intact to assure black Presbyterians of a voice in national church affairs. 
For the time being, the church will maintain offices both in Atlanta, headquarters of the Presbyterian Church in the United States, and in New York. Committees are expected to take several years to merge the boards and agencies of the two denominations. 
There was some talk of reuniting Presbyterians immediately after the Civil War, but serious negotiations did not begin until 1937. By 1954 a plan had been approved, but the widening debate in the churches and the nation over civil rights and concern over theological liberalism in the Northern church led to defeat of the proposal by the Southern church. 
There were no signs of old animosities in the convention halls today. New Doctrine for a Newer World 
One of the tasks of the new denomination will be to write the Confession of Faith. Since the new doctrinal statement will attempt to state the Reformed theology of John Calvin in light of such relatively recent developments as the ecumenical movement, it will be viewed as a major contribution to contemporary Christian thought. 
Older statements of doctrine, such as the Westminster Confession of 1645, and similar documents will continue to be used to explain church teaching. 
Presbyterian theology honors the teachings of Calvin, the Swiss theologian whose Institutes of the Christian Religion expounded doctrines based on the absolute sovereignty of God, the total depravity of man and the ultimate authority of the Bible as a moral guide for the believer. 
Though Presbyterians are willing to accept varied definitions of some doctrines, they have always been wary of straying too far from Calvin's Reformed theology. ''Americans need to remember that John Calvin was one of the fathers of our church,'' said Dr. Charles Partee, professor of history at Pittsburgh Theological Seminary. Communion Interpretations 
The Reformed tradition accepts many of the same creeds as other Christian communions, but Calvin clashed with Luther and other Reformers over doctrines concerning the sacraments. Presbyterians, for instance, tend to describe holy communion as a ''memorial'' of the Last Supper, rather than emphasize the physical presence of Jesus as exemplified in the communion service's bread and wine. 
The doctrinal tenets of Presbyterianism are rooted in the 16thcentury Reformation, but in day-to-day aspects the church is shaped almost totally by its American experience. 
When Scottish and Scottish-Irish immigrants came to the New World in the colonial period, their Presbyterianism sustained them spiritually in the rigorous frontier days. 
They were strong individualists who were uneasy about the Puritan attempt to create a ''Holy Commonwealth'' in the New England colonies, especially because many Scots had been oppressed by the Anglican authorities in Great Britain. Separation of Church and State 
Presbyterians quickly found ways to adapt their church life to the American scene. In 1729, colonial Presbyterians met to approve a significant change in the Westminster Confession, which gave the government the right to convene an assembly of the church. The American Presbyterians replaced that provision with a paragraph that stressed the separation of church and civil authority. 
From the time the first presbytery was formed in 1709, the principle of a representative democracy was deeply rooted in the church. For some, this commitment to democracy carried over into public life. The Rev. John Witherspoon, a Presbyterian minister who came to this country from Scotland in 1768, signed the Declaration of Independence. 
To preserve its teaching, the church emphasized an educated clergy. Because the church was unwilling to send large numbers of theologically untrained lay preachers to frontier missions, Presbyterianism did not grow rapidly in frontier areas during the westward expansion of the nation. 
And so, while the growth of Presbyterianism was slowed on the prairies, the church took root and prospered in established population centers. Largely because of this, three-fifths of the Presbyterians in the denomination created today live east of the Mississippi River and north of Tennessee. 
Six Presidents of the United States were Presbyterians: Andrew Jackson, James Buchanan, Grover Cleveland, Benjamin Harrison, Woodrow Wilson and Dwight D. Eisenhower. 
According to a recent survey of its members by the United Presbyterian Church, 40 percent are professional workers, as against 11 percent of the population as a whole. More than 16 percent report incomes of $50,000 or more, a level achieved by only 9 percent of the general population, the researchers reported. 
''It is an essentially middle-class church which nonetheless accepts a good deal of pluralism,'' said Dr. Samuel Calian, president of Pittsburgh Theological Seminary. 
No similar survey has been taken by the Presbyterian Church in the United States, but its leaders say the composition of their wing is comparable. For Some, Time, but Not Money 
Another survey of United Presbyterians reported that while members said they would willingly give up free time or suffer the loss of friends for the sake of their faith, they were less willing to sell securities or property or take out loans to support a Christian cause. 
The future of the new church may depend on how well it deals with some potentially serious problems in membership. In recent years, membership in the United Presbyterian Church has declined about 16 percent, and it has declined about 10 percent in the Presbyterian Church in the United States. 
The most recent statistics available for the United Presbyterian Church show that three of five members are female, 60 percent are over 45 years of age, and 20 percent are over 60. Members under the age of 35, especially those under 22, make up a conspicuously small portion of the church. 
Dr. Thompson told the general assembly here that the loss of membership in the United Presbyterian church last year, about 36,000, was the smallest in the past decade and 10,000 fewer than the church lost in 1981. 
Baptisms of both adults and infants increased last year, the stated clerk said, and giving to the church appears to be increasing. In creating the new church, ''the past will be a guide, but will not be the final authority,'' said Dr. Andrews. ''We should deliberately try to get something that we know will work today.'' 
''Reformed tradition means we are always reforming,'' said Dr. Calian of the Pittsburgh seminary. ''The emphasis we take should be on the future.''