The U.S. Court of Appeals yesterday upheld the government's proposal to set up listening centers at archives across the country where the public can hear tape recordings made during the administration of President Nixon.

The appeals court, affirming a 1979 decision by a lower-court judge, rejected Nixon's claim that public access to actual copies of the tapes invaded his constitutional rights to privacy and threatened the confidentiality of the executive office.

Nixon had proposed that only transcripts or summaries of the tapes be available to the public, that access be limited to Watergate-related tapes or that release be delayed for several years. He had argued that those alternatives would be less intrusive on his privacy than release of the actual tapes.

The issues in the case yesterday cover Nixon's last remaining dispute with the government over disclosure of the tapes, which have been a subject of court battles since 1974. A settlement agreement reached in 1979 resolved most aspects of litigation on access to Nixon's presidential materials. However, Nixon can still challenge the disclosure of each conversation individually.

Nixon's lawyer, R. Stan Mortenson, said yesterday that he may ask the appeals court to review its decision or take the case directly to the U.S. Supreme Court for review.

Since May, 1980, more than 12 hours of so-called Watergate tapes have been available for listening at the National Archives in Washington.

Regulations approved by Congress prohibit the disclosure of tapes that relate to national security, personal or private matters and other limited areas. But Senior Judge Carl McGowan, writing for the three-judge appeals court panel yesterday, said there was "little force" in Nixon's argument that he had the right, as an individual, to conduct his personal and business affairs without the public watching or listening in and that he expected his affairs to be kept private.

A president's expectation of privacy is undercut by the public interest traditionally attached to presidential materials and by the president's voluntary assumption of his role as a public leader, McGowan said. He was joined in his opinion by Chief Judge Spottswood W. Robinson III and U.S. District Judge Norma Holloway Johnson, sitting on the appeals court by special designation.

The case before the appeals court yesterday stemmed from a 1977 U.S. Supreme Court decision upholding the constitutionality of the Presidential Recordings and Materials Preservation Act, which gave Congress the authority to seize all tapes and other materials accumulated during the Nixon presidency.

The act directed the General Services Administration to set down regulations governing public access to those materials. After unsuccessfully challenging the act itself, Nixon returned to the federal court, in the case decided on appeal yesterday, and challenged the legality of two specific GSA regulations on disclosure of the tapes.

The court also ruled that government archivists can continue to screen hundreds of dictabelts and cassette tapes to determine which ones Nixon used to dictate a personal diary from November, 1971, to April, 1973. Nixon had disputed what he called the "word by word" review of those materials, which must be immediately returned to him once they are identified as diary-related recordings.

The court said that archivists sometimes must listen to the tapes beyond the first few words to determine if the tapes constitute diary material.