More than 6,500 scientists, including a majority of professors in the nation's top 20 university physics departments, have declared themselves opposed to President Reagan's Strategic Defense Initiative (SDI) and have pledged not to accept any "Star Wars" research funds, SDI opponents said yesterday.

The scientists, including 15 Nobel laureates, have signed a "pledge of nonparticipation" which calls SDI "ill-conceived and dangerous." The pledge maintains that no weapons system can render nuclear missiles "impotent and obsolete," as Reagan has called for, and that further pursuit of a missile defense is likely to spur an arms race on Earth and in space.

"What we are witnessing is the third major uprising of the nation's scientists against an element of U.S. weapons policy," Rep. George E. Brown Jr. (D-Calif.) said yesterday. He said the only precedents are scientific opposition to nuclear tests in the atmosphere in the late 1950s and to development of antiballistic missile (ABM) systems 10 years later.

Brown said the opposition to a space-based missile defense shows that Lt. Gen. James A. Abrahamson, SDI director, was incorrect last fall when he said that there were "only a few diehards left, sincere diehards, but only a very few" opposing the program.

"Mr. Abrahamson must have meant a few thousand diehards, or a few tens of thousands, since we can see from the SDI boycott that opposition to the program is firmly established and growing," Brown said.

Attempts to obtain comment from the Defense Department's SDI Organization yesterday were unsuccessful. Last Friday, a group of pro-SDI scientists announced the formation of a Science and Engineering Committee for a Secure World and said they had enlisted 80 scientists to support SDI research.

John Kogut, a physics professor at the University of Illinois-Urbana and a leading SDI opponent, held a news conference yesterday to announce the results thus far of the scientists' campaign against Star Wars research. Kogut was joined by Brown and Philip W. Anderson, a Nobel laureate in physics from Princeton University; James W. Cronin, a Nobel laureate in physics from the University of Chicago, and James R. Melcher, an engineer who heads the Laboratory for Electromagnetic and Electronic Systems at the Massachusetts Institute of Technology.

Kogut said that 57 percent of faculty members at the nation's top 20 physics departments, as ranked by the Chronicle of Higher Education, have pledged not to participate in SDI research. In 109 physics and engineering departments around the nation, more than half of faculty members have signed the pledge, he said.

In total, 3,700 professors and senior researchers and 2,800 graduate students and junior researchers have said they will not take SDI money, Kogut said. He added that all signatories work in fields that will be crucial to SDI research: physics, engineering, applied physics, computer science, chemistry, astronomy and mathematics.

Anderson said the campaign reflects an "extraordinary level of opposition to SDI among working scientists." He said the opposition will certainly complicate the administration's task.

"They can always get the people; the question is, of what quality," Anderson said.

The committee of scientists supporting SDI, led by former Rockefeller University president Fred Seitz, criticized scientific opponents for taking a position "in advance of proper research, experimentation and testing."

The opponents responded yesterday that technical advances are likely, but said they are "likely to induce the other side to increase their offensive forces in an attempt to overwhelm the defense."

"Countermeasures will be followed by counter-countermeasures," they said in a statement. "Star Wars will not be the end of the arms race."