Washington business leaders predicted yesterday that area job losses from the Reagan administration budget cuts would be far less than expected and the private sector would have little trouble absorbing the newly unemployed.

Geico Corp. Chairman John J. Byrne, who headed the special task force of the Greater Washington Board of Trade, told a news conference "much of the press consideration of this issue has been overblown. We don't think large numbers of people are going to be unemployed."

The nine-member blue ribbon panel accepted recent projections by the U.S. Office of Personnel Management (OPM) and a congressional task force showing that 4,400 federal employes will lose their jobs in the Washington area. Earlier studies had predicted job losses of up to 40,000.

The task force report, which was approved by the Board of Trade's directors earlier this week, proposed a two-phase program for coping with the federal employment cuts. A first stage will include a counseling program to help the unemployed workers search for jobs in the private sector and a bid for the cooperation of personnel directors in matching the civil servants to their companies' jobs.

Stage two, Byrne said later, would be triggered only if federal job loss reached around 7,000. In this second plase, the Board of Trade would establish a computerized data bank to match the workers' skills to slots in private business.

Byrne said that if private sector job creation in 1980 and 1981 is "anywhere close" to the levels seen in the previous two years, private business "should be able to gracefully handle a number as low as 4,400." About 37,000 jobs were added by Washington area businesses in 1978 and about 20,000 in 1979.

But Byrne added that the displaced workers' success in finding jobs will also depend on how closely their skills match those needed by business.

"We don't know their GS levels or their skills yet," he said. "We'll have to wait and see what the skill mix will be." Donald J. Devine, director of OPM, said at the news conference that the most difficult to employ will likely be "the upper-graded individuals with skills most unique to government."

Byrne defended the task force's expectations of relatively low federal jobs loss, saying that earlier studies "included a lot of empty slots" that were budgeted but not filled.

Rep. Michael D. Barnes (D-Md.), who heads a congressional task force on unemployment of civil servants, said the estimate of 4,400 used by the Board of Trade "constitutes a sort of minumum projection. Those are the ones we know about now. The numbers could conceivably go up from there." Such higher numbers of unemployed civil servants could be handled by the task force's plan, Byrne said, up to about 7,000. "Beyond that, it's pretty much everybody's guess," he said.

Barnes represents a Montgomery County district thick with civil servants and he requested the Board of Trade study.

Besides insurance executive Byrne, the panel included Vincent C. Burke, chairman of Riggs National Bank; J. Pat Galloway, Board of Trade president and general manager for the Washington area of Sears Roebuck & Co.; Luther Hodges Jr., chairman of National Bank of Washington; Malcolm Lovell, president of the Rubber Manufacturers Association; Edgar S. Mangiafico, chairman of Hecht's; Robert J. Mulligan, vice chairman of Woodward & Lothrop; W. Reid Thompson, chairman of Potomac Electric Power Co.; and John R. Tydings, executive vice president of the Board of Trade.