President Carter, in an unpublished letter to congressional leaders, has voiced strong support for expanding nuclear power and urged development of a breeder reactor demonstration plant more advanced than the controverial Clinch River breeder reactor in Tennessee.

Carter's letter, coming in the wake of the Three Mile Island accident, is certain to sharpen the growing national debate over the future of nuclear power in this country. In particular, it is likely to intensify the efforts of antinuclear groups that are organizing a protest rally in Washington Sunday.

In the April 24 letter, the president renewed his bid to kill the $2.2 billion Clinch River breeder reactor, which was been under development and embroiled in controversy for several years. At the same time, Carter declared:

"I want to emphasize that my opposition to the CRBR does not imply opposition to breeder reactors in general or to nuclear power. Along with developing our renewable energy resources based on solar energy and fusion, breeder reactors hold the promise of providing essentially inexhaustible supplies of electrical energy.

"We need to pursue a vigorous program of breeder reactor research and development so that this option can be commercially available to us if and when we need it."

Carter has opposed continuation of the Clinch River project, which has been plagued with technical problems and huge cost overruns, since the beginning of his administration. On Nov. 5, 1977, he exercised his first veto in an effort to kill funding for the plant. Congress has continued financial support over his objections, however, and the project is costing about $15 million a month.

Administration leaders have been deeply divided on how to resolve Carter's fight with Congress over Clinch River. Some have advocated a compromise offer that would state an expectation, though not a commitment, to build a test breeder, instead of the currently planned commercial power producer, at Clinch River beginning in fiscal 1982.

Carter has rejected that approach, however. Signing off on a March 26 memo, he scrawled in the margin:

"I would rather go down swinging. A large breeder in the near future is a waste of money. JC."

Nonetheless, the breeder reactor facility that Carter advocated in his letter to congressional leaders would be far more complex and larger than the current Clinch River facility, administration sources said.

A "breeder" reactor gets its name from the fact that, in "burning" uranium, it produces substantial amounts of plutonium or other fissionable material, which can itself be processed into additional fuel for the reactor. Thus, in effect, such a reactor "breeds" or generates more fuel than it uses, unlike a conventional atomic power plant which must be refueled with new supplies of processed uranium.

Advocates of nuclear power have argued that the breeder will be an indispensable bridge between existing reactors, uranium for which may become scarce later in this century, and fusion power, which is not expected to be available until well into the 21st century.