Southern Presbyterians overwhelmingly approved a plan this week that would reunite them with the larger United Presbyterian Church and close a breach dating from the Civil War.

Meeting in Columbus, Ga., delegates to the General Assembly of the 840,000-member Presbyterian Church in the United States, as the Southern church is properly called, voted 344 to 30 to merge with the 2.4-million member United Presbyterian Church in the U.S.A. The size of the margin was a surprise to both supporters and opponents of the proposal, on which leaders of the two churches have been working for nearly a decade.

The merger proposal now goes to the UPCUSA General Assembly, scheduled to meet next week in Hartford, Conn., where approval is widely expected. The proposal then goes to the presbyteries, as the local clusters of congregations are called, of each denomination, where it must be approved by three-fourths of the PCUS and two-thirds of UPCUSA presbyteries.

The two churches split in 1861 over the issue of slavery. But in recent years the church union movement has brought increased cooperation between the churches, which share the same theological and historical bases and the same form of organization and government. In 16 communities, including Washington, local churches of the two denominations have anticipated merger of the parent bodies by joining in union presbyteries.

Neither denomination has escaped the controversy over biblical literalism and traditional expressions of Christianity that has swept Protestantism in recent years. The Southern or PCUS church was hardest hit in 1973, when several hundred congregations, most of them with fewer than 100 members, broke away and formed what is now known as the Presbyterian Church in America.