President Carter cast the first veto of his nine-month-old administration yesterday, rejecting a bill authorizing $80 million for the Clinch River nuclear breeder reactor.

In returning the legislation to Congress, Carter said approval of the project would seriously imperil efforts "to prevent the proliferation of nuclear weapons and nuclear explosive capability" around the world.

It would also, he said in a strongly worded message, saddle the United States with "a large and unnecessarily expensive project, which, when completed, would be technically obsolete and economically unsound."

It was the 2,356th veto in U.S history, and Carter's chief domestic adviser, Stuart Eizenstat, said he is "very hopeful" it will be sustained. It takes a two-thirds majority in both houses of Congress to override a presidential veto, something that has been done only 90 times since 1792.

The veto comes at a time when the administration's energy package is locked in a House-Senate conference committee on Capitol Hill. But Eizenstat said he was confident the move wouldn't have an adverse impact on the energy program because "we've made it clear from the beginning of the administration that the President is against the Clinch River project."

However, he was unwilling to speculate if Carter will veto an appropriations bill, containing funds for the Clinch River bredder as well as other projects, which has yet to reach the President's desk.

The vetoed bill would have authorized or given permission, for the project to proceed; the pending measure would provide the money to do so.

During the last six months, the battle over the Clinch River project has become a symbolic fight on the future of nuclear power development. The project is a government-industry venture at Oak Ridge, Tenn., designed to demonstrate the breeder process on a large, commercial scale.

A successful fast breeder - generating heat to drive a turbine - has been a scientific dream sinc the start of the nuclear age. Its purpose is to produce electricity without oil, coal and gas, all in scarce supply. Instead of using up nuclear fuel in the process, as a uranium reactor does, it would produce more nuclear fuel than it consumes. The by-product fuel produced is plutonium, however, which can be converted for use in atomic bombs.

Senate Foreign Relations Committee Chairman Frank Church (D-Idaho), one of the project's advocates yesterday called the veto a "rereal from reality."

"Other nations have already crossed the threshold of the plutonium age," Church said. "The French are building a huge commercial breeder reactor in which the West Germans and the Italians share. The British have on even larger one on the drawing boards, and the Russians built their Clinch River breeder reactor years ago."

In his veto message, Carter, a former nuclear engineer, said the cost of the project had grown from an estimated $450 million when it was first authorized in 1970 to more than $2.2 billion. He said he intends to pursue all authority at his disposal, including impounding funds, to stop contruction of the project.

"I am committeed to a vigorous energy research and development strategy to ensure maximum progress on shifting the energy base of the United States away from oil and natural gas," he said. "However, I am also concerned about the risk of introducing the plutonium economy through an unnecessary commercial demonstration facility."

He also said the bill authorizing the project would:

Put burdensome limitations on the President and the new Energy Department indeveloping an effective energy research program.

Encroach on presidential authority through three provisions that would have permitted one chamber of Congress to veto presidential actions.

Unwisely limit U.S. ability to impliment his new policy on spent nuclear fuels.

In distributing Carter's two-page veto message domestic adviser Eizenstat attempted to minimize the impact of vetoing a bill passed by a Democrat-dominated Congress. The fact that this was the first veto since the President took office on Jan. 20, he said, demonstrated "the considerable cooperation" that has existed between Carter and the Congress.

During a similar period in office President Kennedy vetoed five bills passed by a Democratic Congress, he said.