A potentially far-reaching dispute has broken out between the Navy and the University of Rochester over the Navy's threat to cancel Rochester's 16-year stewardship of the Center for Naval Analyses unless the university lets the Navy name the center's president.

Secretary of the Navy John F. Lehman Jr., according to university president Dr. Robert L. Sproull, wants the current CNA president fired and replaced by former assistant secretary of defense Francis J. West, who left his Pentagon post a few weeks ago.

Sproull, who is chairman of the board of overseers of CNA, has rejected the Navy's demands.

He also has complained in a March 4 letter to Deputy Secretary of Defense Paul Thayer that such actions threaten the credibility of all six federal contract research centers (FCRCs), which are supposed to give the services independent, unbiased assessments of their operations, strategies and programs. He said that Thayer has not replied.

At issue is a Navy demand that it be allowed to select the CNA president, with university approval. Until now, the university has chosen the president, subject to Navy approval.

"That difference is enormous," Sproull said in a telephone interview yesterday. "No other FCRC has ever been asked to do that. We have been told that we will not be the contractor any longer after September 30 when the current annual contract expires unless we agree."

"A great deal is at stake here," Sproull said. "This means the Air Force presumably could force" the Rand Corp. to perform differently under such threats.

CNA concentrates on analyzing Naval exercises to see how ships and tactics perform. The five other FCRCs are the Institute for Defense Analyses, which provides evaluations for the Secretary of Defense, and four think-tanks that specialize in Air Force problem-solving: Rand, Aerospace Corp., Mitre Corp. and the Lincoln Laboratories, run by the Massachusetts Institute of Technology.

All of these centers, Sproull said, "are managed by competent boards outside of government."

Included in the Navy's demand for change, Sproull wrote to Thayer, is "Secretary Lehman's desire to have Mr. Francis J. West Jr. replace Mr. David B. Kassing as president of CNA . . . within a few months."

Sproull says that while CNA had "tried to be accommodating" and offered other posts for West, the board of overseers found "no cause" to replace Kassing, who has headed CNA since 1973.

West also has considerable experience in naval matters.

"We are all in favor of a strong U.S. Navy," Sproull said in an interview, "but this is pretty fundamental. The issue is whether responsibility and authority go to the same place. When the Navy contracts with Boeing, it doesn't tell Boeing who their president should be.

"If the president of CNA is designated by the secretary of the navy, that will influence the staff and then how do you get any credibility for those analyses when they go to Congress or the secretary of defense?" he asked.

In his letter to Thayer, the university head warned that the Navy's action "poses a dangerous precedent" for the other FCRCs, that the credibility of their unbiased work "could easily be destroyed." He said that "the university is not willing" to continue as the CNA contractor under such arrangements.

The CNA, headquartered in Alexandria, has about 275 employes worldwide and operates under an $18 million annual contract.

Sproul and Kassing say that the dispute with the Navy has been simmering for months, but that they have had no indication that the Navy was unhappy with the center's work or its leadership.

But Kassing notes that there were "rumors about the political background of some people" hired by the CNA in the past two years, particularly two officials who had worked for the Carter administration.

This was a reference to Robin Pirie, a Naval Academy graduate who had been an assistant secretary of defense under Carter, and Bernard Rostker, a former Rand economist who was head of Selective Service under Carter.

A spokesman for Lehman, asked yesterday for comment on the CNA situation, did not respond.