The trustees of George Washington University voted yesterday to try to sell or lease the university hospital to a profit-making firm and invited major companies to bid for it.

Officials said the decision, approved by the board after a year-long study, was prompted by the need to raise millions of dollars to modernize the 37-year-old hospital at Washington Circle NW, which treated President Reagan after an assassination attempt almost four years ago.

They added that the hospital's operating surplus had dwindled recently because of changes in Medicare reimbursement rules.

Although the move would be the first of its kind in the Washington area, about 10 teaching hospitals across the country have been purchased or leased by private firms during the past year. Locally, Georgetown University has been exploring the possible sale of its hospital, but has not yet announced a decision.

"We don't feel the university itself can generate the capital that will be needed in the next five years to keep [its] hospital at the top . . . without some kind of help from outside," George Washington president Lloyd H. Elliott declared. He said that the university would "maintain control over policy and operations" and that the hospital would continue its programs in medical education, research and indigent care.

Yesterday, spokesmen for two firms, Hospital Corporation of America and American Medical International, said they will submit proposals to the GW board.

Although the university put no price tag on its 511-bed facility, a spokesman for AMI said its value would probably be "in excess of $100 million."

Last year AMI paid $108 million for a 500-bed hospital in Omaha, affiliated with Creighton University, while Hospital Corporation paid $265 million for an 800-bed facility affiliated with the University of Kansas in Wichita.

Across the country the number of for-profit hospitals has increased substantially over the past decade, and currently totals about 1,200 out of about 5,800 institutions. The trend has aroused criticism by some doctors, labor unions, and community groups that the firms raise the price of medical care but reduce the quality of care, charges that the hospital companies strongly deny.

However, since the GW trustees announced in October 1983 that they would study the possibility of selling the hospital, there has been little criticism of the move. Dr. Ronald P. Kaufman, GW's vice president for medical care, said physicians at the hospital were involved in setting the conditions for a possible sale or lease.

Yesterday spokesmen for two health care activist groups criticized the trustees' decision. Cheryl Fish, director of the Coalition for Financial Accountability, said that under new ownership the hospital "may take actions to discourage Medicaid patients from coming." Joni Eisenberg, coordinator of the ad hoc D.C. Health Care Coalition, said that "When the for-profits move in, health care costs increase for the whole community. We as a coalition are trying to educate the public and safeguard ourselves."

Last year Kaufman said the hospital needs about $30 million for major renovations in the next few years "just to keep up to speed." In less than 20 years, he said, it would probably have to be replaced at a cost of "well over $100 million."

Elliott said it would be "very difficult" to raise such funds because the federal government has stopped providing aid for hospital construction and private philanthropy for hospitals has "dwindled." The other alternative, he said, would be borrowing the funds, either through tax-exempt bonds or from private lenders. But he said it was increasingly difficult to carry such large debts, particularly since the new Medicare rules set fixed fees rather than reimbursing hospitals on a cost-plus basis as most insurance plans have in the past.

The planning study for the possible sale was conducted by the university in cooperation with AMI, which is based in Beverly Hills, Calif. However, university officials said yesterday that they were not committed to making an agreement with that firm and would accept the best offer received. The other firms from which proposals are being sought -- all of which must own at least 50 hospitals -- also include Humana, whose hospital in Louisville recently was the site of a mechanical-heart implant; National Medical Enterprises, of Los Angeles; and Republic Health Corp., of Dallas.

Under the specifications outlined by the trustees, the hospital would be controlled by a seven-member governing board, with four members appointed by the university president and three named by the company. If there are "unforeseen difficulties," the trustees said the university could buy back the hospital at any time.

Any change in ownership would require approval by the District government's health planning agency.