The General Accounting Office has questioned the Veterans Administration's long-standing claim that it is cheaper for the federal government to operate a national network of VA health-care facilities than to send veterans to commercial hospitals.

The GAO said it found several "flaws, questionable assumptions and errors" in the methodology the VA used when it told Congress last year that the cost of health care at VA hospitals in 1982 averaged 15 to 19 percent less than comparable care in commercial hospitals.

The VA overstated charges at commercial hospitals and underestimated charges at its own facilities, the GAO said. The VA's cost comparisons had so many errors that its conclusions were invalid, according to the government watchdog agency.

The cost of VA- versus commercial-hospital care has been a sensitive subject since 1977, when the National Academy of Sciences recommended to Congress that the VA slowly phase its facilities into the commercial health care system.

The VA operates the largest hospital network in the country, a $7 billion-plus operation that includes 172 hospitals, 226 outpatient clinics, 95 nursing homes and 16 extended care facilities. About 194,000 of the agency's 220,000 employes are in the health-care delivery field.

Since the academy of science raised the "mainstreaming" question, the VA has conducted several cost comparisons for Congress, all of which showed that the agency's system was cost-effective. The most recent report came after a group of environmentalists and physicians in Portland, Ore., sued to stop construction of a $153 million VA hospital in their area.

A judge ruled against the group, but several physicians involved in the dispute asked the American Medical Association to pass a resolution in support of mainstreaming. The AMA refused, but urged the VA to study the idea.

James A. Christian, an executive assistant to the VA's chief medical director, said the VA cost-comparison studies were as "accurate as possible based upon available data."

The cost of care at commercial hospitals rose an average of 11.5 percent in 1981, Christian said, but the increase at VA facilities was 8.3 percent. He said care provided by VA facilities also is more extensive than at many commercial hospitals because 91 percent of the VA's acute care and surgery hospitals are affiliated with medical schools.

Mark Adelman, who wrote the most recent VA report, said it was hard to compare the two types of hospitals. He said many patients at VA facilities don't see a doctor until they come to the hospital, while patients at commercial hospitals are admitted only after their family doctor has tested and examined them. This makes it hard to estimate the cost of doctor services in a hospital.

The GAO's sharpest criticism was that the VA had not considered the impact of closing a VA hospital. A closing, the GAO said, might lower the cost of care in some areas. Adelman said a study would cost more than $4 million and "we feel that money is better spent on patients."