President Reagan has rejected Engery Secretary James B. Edwards' request that the federal government bail out an idle $350 million nuclear reprocessing plant in Edwards' home state of South Carolina, but he also made it clear that he would not seek to curb such reprocessing by private firms.

National concerns over the spread of weapons-grade nuclear material spurred Reagan's predecessor, President Carter, "defer indefinitely" federal funds to support reprocessing by private companies. As a result, the South Carolina plant, located near Barnwell and partly completed six years ago, has never been operated.

Reagan told Edwards in a private memorandum, written March 20 and released yesterday by the White House, that while he does not "believe it would be appropriate for the federal government to acquire the Barnwell plant or to finance construction or operation of any of its facilities," he wants the energy secretary to "develop recommendations for my further review on how to create a more favorable climate for private reprocessing efforts."

Reagan added in the memo: "I wish to emphasize that the Department of Energy should consult with industry to determine which regulatory barriers are of greatest concern to it. . . ."

The decision was clearly a setback for Edwards, who has conducted a campaign of sorts on Capitol Hill and in the nuclear industry to win support for an outright government purchase of the Barnwell plant, which is owned by Allied General Nuclear Services, a partnership of Allied Chemical Corp. and a company owned by Gulf Oil Corp. and Royal Dutch Shell.

But a department spokesman said yesterday that, "We interpret the memo as being a strong message of support for nuclear reprocessing."

The Barnwell reprocessing plant was designed to receive spent uranium fuel from nuclear reactors around the country and to reclaim from that fuel reusable uranium and plutonium, a byproduct of the reaction.

The market for the uranium was to be the same nuclear reactors, where the recycled uranium could be burned again. The plutonium was to be burned in a new generation of "breeder" reactors.

The corporate owners of the Barnwell plant are currently trying to position themselves to supply the initial plutonium fuel needs of the breeder reactor program, which Reagan has promised to revitalize. President Carter essentially stopped development of the breeder in 1977 by cutting off funds for the Clinch River demonstration reactor near Oak Ridge, Tenn.

"There is just no way private enterprise can operate in an environment where there is not a free market," said James Buckham, chief executive of Allied General. "There is only one customer for plutonium and that is the federal government. The Reagan administration has funded the breeder and the first one or two plants are going to need the output of Barnwell to supply those breeders."

The Barnwell plant has kept its doors open since 1977 because Congress has appropriated about $12 million a year for research into how to manufacture "proliferation resistant" plutonium and how to safeguard plants that make nuclear material.

As the nuclear industry fights for a comeback, the profitability of reprocessing without government assistance is likely to face the renewed skepticism of its critics.

Th debate over security will most likely return also. Government and private studies have raised doubts about the ability of the reprocessing industry to protect small quantities of plutonium from being taken by force or subterfuge by terrorists. A few pounds of plutonium produced in reprocessing can yield a small nuclear bomb.