New medical methods have led to a sharp increase in both the frequency and the success of human organ transplants, making possible for the first time 5,000 kidney transplants and more than 100 heart transplants last year.

Still, the number of organs available for transplanting is "tragically inadequate," because 20,000 men, women and children each year in this country need a transplant to survive, health officials said today at a conference here.

A new drug, cyclosporine, has cut dramatically the rate of organ rejection by the body's immune system. At the same time, doctors can better match organs to recipients.

Health officials called for a high-pressure nationwide advertising campaign--including half-time commercials during televised football games--to make donations of hearts, kidneys and livers a "natural and expected" part of death.

This agreement on the need for intensive public education came at a meeting convened by U.S. Surgeon General C. Everett Koop, who hopes to convince the public, doctors, nurses and other health workers that organ transplants are a "gift of life" that can give "real solace" to survivors. In only 2,200 cases did Americans last year agree to donate one or more major organs of dying relatives to help some of the 20,000 persons needing them.

Koop also pledged to convene a working group soon to organize a new non-governmental federation or council to help make transplants more common.

He said he will order the National Institutes of Health to organize a group of doctors and scientists from several NIH institutes to find methods to make sure that several usable organs can be removed from the same donor.

Transplant surgeons said doing this is one of the most obvious ways to increase the organ supply, yet the chance is often missed. What doctors have to learn, Koop said, is "don't just take the kidneys and waste livers and hearts, and vice versa."

The 45 conferees at the Project Hope Health Sciences Education Center included several of the nation's top transplant surgeons and hospital transplant coordinators, as well as patients seeking donations.

Anne and Bryan Vossequil--he is a Secret Service agent who soon will be assigned to the White House--told how their 13-month-old son died last October after six disappointing months on a waiting list for a donated liver. Raymond White of Nashville said his wife, a Presbyterian minister, has waited 16 months for a donated heart. "Please have a sense of urgency in what you do," White told the conference.

Donald Denny, the University of Pittsburgh's organ procurement director, said it is often other doctors who fail to tell transplant surgeons that their patient is dying or "brain-dead" and on a respirator--when the organs could be removed in good condition if death were sure--or who fail to ask the surviving family for the organs.

"The well-meaning family doctor often wants to spare the family more pain by making the request, when actually it's just the opposite," Denny said. "In our area, 82 percent of all families asked quickly say yes."