President Carter suffered a sharp setback yesterday when a key Senate committee rejected his choice of Massachusetts Institute of Technology nuclear engineer Kent F. Hansen to be the fifth member of the Nuclear Regulatory Commission.

Hansen was rejected 7 to 4 by the Senate Committee on Environment and Public Works after members objected that he lacked experience in nuclear regulation and was insensitive to safety questions.

At the same time, Carter's emphasis on prohibiting the spread of nuclear weaspons gained fesh support on Captitol Hill when key senators and members of Congress appeared in favor of a plan the administration will announce today to take over ownership of spent nuclear fuel. The administration's plan would include domestic and foreign fuel, which it would store in a facility owned by the government pending enactment of a policy to reprocess the spent fuel or bury it permanently.

The policy to be announced today means the United States would take title to nuclear fuel once it is spent, Storing it for an indefinite time for a one-time fee to be paid by the fuel user. The fee has not been determined but is understood to be less than $10 million for a complete nuclear fuel core.

Hansen, an MIT engineer, was a personal choice of Energy Sercretary James R. Schlesinger for the fifth spot on the NRC. The 2,600-person commission is charged with licensing atomic power plants and overseeing safety and environmental questions associated with nuclear energy.

Sen. Gary W. Hart (D. Colo.) said Hansen was turned down by the committee because he exhibited "a noticeable absence of thought, background and depth on such questions as safety and waste disposal."

Hart chairs the Subcommittee on Nuclear Regulation and last Tuesday sent a letter to all committee members opposing Hansen's nomination.

"My opposition to his nomination is based on his lack of experience in policy matters," Hart said in the letter to committee members. "In the coming months, the NRC will face many important policy decisions - licensing reform, plutonium recycling, pending licenses for light water reactors and the controversial breeder reactor. Dr. Hansen's lack of experience in addressing these policy questions would seriously impede is performance as commissioner."

Hart also said he was worried about a "possible appearance of conflict of interest" because Hansen had been employed as a consultant to Westinghouse Electric and General Electric on nuclear matters. Hansen is an expert in the physics of atomic power cores, which Westinghouse and GE build.

"This movement of individuals back and forth between regulatory agencies and the industries they regulate." Hart said, "has cretated a serious problem of public credibility."

Sources said that Hansen's rejection by the Senate committee means almost surely that the Carter administration will withdraw the nomination rather than take it to the Senate floor. The rejection leaves what amounts to a 2-2 split on key NRC votes.

The Commissioners include Victor Gilinsky and Peter Bradford, who often oppose industry positions. The other two are NRC Chairman Joseph Hendrie and Richard Kennedy, who are generally thought to be pro-industry on some positions.

The key questions surrounding the spent fuel policy to be announced today is whether or not the administration will insist the fuel storage facility be subject to licensing by the Nuclear Regulatory Commission.

Capitol Hill sources said yesterday they might oppose a spent fuel policy that did not require a license for the storage site because it "takes Congress out of the decision-making process."

The spent fuel policy is sure to raise questions about where the storage site is built and who runs it. Some public advocacy groups were already questioning whether the Carter administration would revitalize closed industrial reprocessing plants, like Allied Chemical's Electric's facility at Morris, Ill.

"The question now is whether it is a bailout," said Jim Cubie of New Directions, a public advocacy lobby. "They question now is: Do the utilities pay the full cost? We're worried that it will be a subsidy."

Spent nuclear fuel contains isotopes of uranium like plutonium that can still be used to generate power. Recovery of the plutonium which can be used to make bombs, raises the spectre of a possible spread of nuclear weapons.

Spent fuel is today stored by electric companies in huge pools of water alongside the power plants. An estimated 2,500 tons of spent nuclear fuel is stored this way at power plants sites and another 99 applications are before the NRC to expand storage sites at 44 plants.

Estimates are that spent fuel in the United States will grow to 7,500 tons in five years and 20,000 tons in 10 years. One-third of all the nuclear fuel being burned every year becomes spent fuel.