The $74 billion Farm Credit System could lose between $2.6 billion and $7.4 billion in the year ending next June -- enough to threaten the viability of the entire system, according to a General Accounting Office study released yesterday.

The GAO report cautioned that its estimates are based on extrapolations from past trends and that the actual outcome might differ. However, some parts of the report indicate that GAO believes that matters are more likely to end up worse rather than better.

"The continued viability of the system depends on whether the trend of growing loan losses can be reversed over the relatively near term and there is little to indicate that this will occur," the report said.

The Farm Credit System, or FCS, is an amalgam of 37 banks in 12 districts and hundreds of local area associations that lend money to farmers, farm cooperatives and other persons in rural areas. It raises money to lend by selling securities to the public. No federal government money is involved and the securities are not guaranteed by the government.

According to the GAO report, the system's earned surplus of $6.3 billion as of June 30, could be wiped out by the middle of next year if the FCS were to make the same allowances for bad loans as do commercial banks. Even if it continues its current policy of setting aside a smaller loan loss reserve relative to the amount of loans on which neither interest nor principal is being paid, the system's surplus could drop to $3.7 billion by mid-1986.

Ron Erickson, a spokesman for the Farm Credit Administration, the federal agency that regulates the Farm Credit System, said he believed the GAO findings were overstated. "We take exception to the fact that these numbers are extremely high," Erickson said.

However, as of this week, the FCS banks were still reviewing their loan portfolios to try to find out just how bad the situation is. Representatives of the system are expected to disclose their own projections of potential losses next week when they testify at a congressional hearing on whether FCS needs federal financial help and, if so, how much.

Donald E. Wilkinson, head of the Farm Credit Administration, said recently that the system cannot remain viable without getting such help within the next two years.

The system currently has a net worth -- earned surplus and capital -- of around $11 billion. It is owned on a cooperative basis by the farmers and others who have borrowed from it. Treated on a systemwide basis, it is among the largest financial institutions in the nation.

The GAO examined trends in the system since 1979 and projected financial performance over the next year. "The earnings picture looks awful," Craig Simmons, a GAO financial analyst, said. "Earnings are eroding, loan losses are mounting, and there's no prospect for it to turn around given the currrent state of agriculture."