The Reagan administration, looking for ways to cut Medicaid costs, has given states the green light to require the adult children of low-income nursing home patients to pay part of the cost of their parents' care.

The new federal position has been applauded by the National Governors' Association, which has long urged that states be given greater power to recoup Medicaid costs, but has been attacked by advocacy groups for the elderly.

Rep. Henry A. Waxman (D-Calif.), chairman of the House subcommittee with jurisdiction over the Medicaid program, said yesterday that the new directive, issued last month, violates the 1965 Medicaid statute by using "legal sophistry that would make a con artist blush."

He also denounced the administration for making a fundamental policy change without seeking legislation or going through the process of formally promulgating a regulation, and vowed to conduct hearings on the matter.

Toby Edelman, a lawyer with the National Senior Citizens Law Center, said yesterday that she believed it is "inevitable that this thing will wind up in court as soon as any state tries to enforce it."

At least three states--Indiana, Virginia and Georgia--have passed laws that would give their Medicaid agencies the power to require contributions from families of nursing home residents whose care is currently financed entirely by the Medicaid program. None, however, has begun to enforce its law.

There are no firm figures on how much would be saved under such a "relative responsibility" approach to Medicaid payments; it would depend on how many states chose to take advantage of the new federal directive and how aggressively they enforced it.

At present, nursing home care for the elderly is the most expensive single component of the Medicaid program, costing $16 billion in fiscal year 1983, with the federal government picking up 55 percent of the cost and the states paying the rest.

The 1965 statute creating the Medicaid program, which provides medical care for the poor, prohibits the federal government from forcing children to be financially responsible for the medical care of their parents. The only "relative responsibility" allowed under the statute is spouse-to-spouse and parent-to-child.

A spokesman for the Health Care Financing Administration, the arm of the Department of Health and Human Services that oversees payments for Medicaid, said the new policy was set forth last month as a clarification in a manual to state Medicaid agencies.

Deputy Director Daniel Bourque said the agency had been considering seeking either new legislation or proposing a new regulation, but that "we looked into it and discovered we had the authority to clear this up."

Another spokesman for the agency, Len May, said the directive does not violate the Medicaid statute because states would still be required to provide Medicaid coverage to low-income nursing home residents if they couldn't collect payments from children or other relatives.

"This isn't an eligibility requirement," May said. "It is an effort to give states the flexibility to recoup some of their costs."

"The theory of holding family members responsible for a portion of the cost of care of their elderly parents sounds good, but the application is fraught with problems," said Elizabeth A. Taylor, a spokeman for the National Citizens Coalition for Nursing Home Reform.

"What about situations where children live out of state?" she asked. "What about situations where children will simply refuse to pay? What about situations where some children are willing to pay and others aren't? It will wind up that relatives who don't want to pay won't be forced to, and that doesn't seem very equitable."

She also noted that the average age of the Medicaid recipients in nursing homes is 81, meaning that their children are often elderly themselves.