A group of businessmen and educators, trying to improve America's competitive position in the world market, took their campaign to the White House yesterday to enlist President Reagan's support.

They received a warm welcome but got no commitments, according to participants in the 15-minute session.

Robert Anderson, chairman of the Rockwell International Corp., said yesterday that the president thanked them for their work in developing a report entitled "America's Competitive Challenge," but said nothing about carrying out its recommendations.

The report calls on the president to make a "major national address" to focus public attention on the need to enhance industry's ability to compete with foreign interests in developing and marketing new technologies. It also asks for the appointment of a presidential adviser on economic competition.

"The report seems to have struck a responsive chord," Anderson said after the meeting. "Our view is that we are not for protectionism, we are not for a governmental planning board" to direct industry effort. "We have the muscle and determination to do the job, but some restrictions have been placed on us."

Anderson and David S. Saxon, president of the University of California, headed the task force of the Business-Higher Education Forum that produced the report.

Among other things, it calls for relaxing trade, antitrust and regulatory restrictions that, group members have said, hinder American industry's ability to take advantage of developing technologies in computers, lightweight metals and genetic engineering.

Task force members have cited recent examples of cooperative research and development projects among competing firms, or joint university-business research projects, as a means of enhancing industry's ability to develop and exploit inventions.

Anderson, Saxon, and seven other members of the task force, including Philip Caldwell, chairman of the Ford Motor Co., and the Rev. Theodore M. Hesburgh, president of University of Notre Dame, also met with Edwin L. Harper, Reagan's assistant for policy development, presidential science adviser George A. Keyworth II and several high-ranking Commerce Department officials.

These sessions also were long on compliments and short on specifics, according to several participants.

"We're all for this effort, but when it comes down to specifics, it's a matter of looking at each one separately," said Robert G. Dederick, undersecretary of commerce for economic affairs.

"This report is not going to sit on a shelf," Gerald J. Mossinghoff, commissioner of the U.S. Patent and Trademark Office, was quoted as telling the group.

Two weeks ago, task force members told the same story to members of Congress and newspaper editors in the hope of dispelling what several task force members see as ingrained public suspicion of corporations.

"The public is not sure this is going to be in the national benefit," William O. Baker, retired chairman of Bell Telephone Laboratories, said in an interview last week. "They wonder if industry doesn't have a special interest."

"I would be enormously encouraged if we could inject a sense of reality and currency into this arena," Baker added. "International competition is here. It is manageable . . . , but we don't have much evidence on action."

"We must find ways" to put the question of competitiveness "at the top of the national agenda," Anderson told Washington Post staff members two weeks ago.