Medicare benefit cuts the Senate Finance Committee approved Thursday were quickly denounced by hospital and insurance groups yesterday, as well as by the nation's largest organization of the elderly.

The Finance bill, it is estimated, would cut Medicare outlays by $13.6 billion over the next three years, the largest single cut likely to be made under the budget resolution the House and Senate agreed on earlier this week.

Neil Swan, spokesman for the Health Insurance Association of America (HIAA), said that such cuts, while they would reduce federal budget deficits, would only force hospitals to raise rates for non-Medicare patients.

HIAA, made up of the nation's major private insurers, says that Medicare already pays hospitals less than the true costs of services to Medicare patients, and the hospitals recoup these losses by charging non-Medicare patients--insured by HIAA members--more.

Swan said that about $5.8 billion in Medicare costs were shifted to non-Medicare patients in 1982 and provisions in the Finance bill putting new limits on Medicare reimbursements will only push this up.

Mike Bromberg, director of the Federation of American Hospitals, the organization of private for-profit hospitals, said, "We don't like some of the short-term cuts" in hospital reimbursments.

The American Hospital Association, which also doesn't like some of the cuts in hospital reimbursements, said that it would fight them in the Ways and Means Committee, where a subcommittee headed by Rep. Andrew Jacobs Jr. (D-Ind.) is to take up Medicare cost control next week.

Hospital groups were able to kill hospital cost control bills in the Carter administration.

Bromberg said his group favors a so-called prospective payment system, under which hospitals are paid preset amounts for various services rather than one where costs are added up after the fact. The Finance bill would eventually effect such a set-payment system.

But Bromberg said another hospital cost-control measure in the bill, limiting reimbursments to hospitals when cost increases exceed 10 percent a year, is unacceptable.

The American Association of Retired Persons (AARP), the largest organization of the elderly, yesterday began an effort to kill many of the cuts.

Its legislative representative, Laurie Fiori, said the AARP was concerned with cuts in reimbursements to providers of medical services, which can be shifted to patients, and also with provisions in the Senate bill that would increase--by $1.2 billion over the next three years--what the patient must pay out-of-pocket for doctor bills and premiums under Medicare.

Jacobs, in a telephone interview from his Indianapolis office, said that he doubted his subcommittee would accept cuts as high as the Senate's $13.6 billion and that he especially opposed provisions that would add directly to patients' out-of-pocket costs.