An estimated 59,000 older persons in the Washington region are falling for insurance company pitches and wasting hundreds of dollars a year on unnecessary, duplicate health insurance policies, a watchdog senior citizen group contended yesterday.

The United Seniors Health Cooperative said 25 percent of the older persons with private insurance to supplement Medicare have at least two policies, when one would be sufficient.

"Get rid of them," said Esther Peterson, a consumer affairs official in the Johnson and Carter administrations and the board chairwoman of United Seniors, which was kicking off a campaign urging that older persons eliminate unnecessary insurance coverage.

Richard Coorsh, spokesman for the Health Insurance Association of America, the leading trade association for the nation's health insurers, said in an interview that the insurance industry itself "believes that generally, most people need just one comprehensive Medicare supplemental policy."

Asked how some senior citizens end up with more than one Medicare supplemental policy, commonly known as Medigap policies, Coorsh said the association had no data on that.

Duplicate coverage is the flip side of a more frequently discussed problem in the U.S. health care system. Many hospitals say they are losing money because of the cost of uncompensated patient care in an era of guns and violence. In the meantime, many employers have cut back medical benefits because of rising costs. Millions of Americans, many of them children and youths, are without any insurance.

Most older people have no coverage for long-term care, such as that provided by nursing homes. But unlike younger Americans, they are able to cover many of their hospital and doctor bills with Medicare. The problem is that they often buy too much insurance to cover the gaps in Medicare, the United Seniors said.

New federal legislation, effective in January, is intended to help end consumer confusion in the Medigap market by forbidding the sale of duplicate coverage. But that won't help seniors who already have duplicate coverage, said United Seniors President Jim Firman.

By dropping duplicate policies, seniors could save an average of $350 to $1,250 a year, depending on how many excess policies they have, the cooperative said.

United Seniors based its conclusions on a study of demographic data from the Greater Washington Research Center, a national survey by the American Association of Retired Persons and its own case records.

One Falls Church couple, both in their seventies, was able to save nearly $6,000 on their annual insurance bills by eliminating unnecessary coverage, Firman said.

Annie M. Costner, 77, a retired Falls Church first-grade teacher, recounted yesterday how troubled she was by the insurance agent who insisted that she and her husband, William, write a check for $2,000 to cover the premium on one of their policies.

"We couldn't afford that," Costner said.

The incident in early 1988 led the Costners to have their coverage reviewed by a counselor with United Seniors. At that time, the couple was spending nearly $8,000 a year on supplemental health insurance.

Acting on the counselor's recommendation, William Costner dropped three Medicare supplemental policies, saving $4,913 in annual premiums. Annie Costner dropped her extra coverage, saving $1,074. William Costner, a postal worker, died in 1989.

Annie Costner, who now lives in North Carolina, came back to Washington yesterday to help start the United Seniors' campaign.

Firman said the public education campaign reflects a recent decision by his group to offer assistance with the increasingly costly problem of health insurance.

Private medical insurance rates for Washington area senior citizens began rising by as much as 35 percent this year because of the repeal of federal catastrophic health coverage and the increase in medical care costs, insurance officials said.