Labor Secretary Ray Marshall said yesterday he expects the nation's unemployment rate, which has been rising rapidly as a result of the recession, to peak at about 8.5 percent early next year.

The rate jumped from 6.2 percent in March to 7.8 percent in May, and the latest figures for initial claims for unemployment benefits indicate layoffs are continuing across the country.

Nevertheless, Marshall said he opposes any general expansion of federally funded jobs programs or across-the-board tax cuts to stimulate the economy.

The Labor secretary called the current level of unemployment "horrible," but said most of the recent layoffs have been concentrated in the auto, steel and construction industries.Stimulus programs aimed at those industries might be warranted, he said, adding that the president has not yet considered any such proposals.

"You have to try to fit the remedy to the nature of the problem," Marshall declared. "The overall rate (of unemployment) could be over 10 percent and you still would not need a general stimulus program if the rate is not pervasive" in the economy.

Meanwhile, the Commerce Department revised upward its estimates of how well the economy performed in the first three months of the year.

The gross national product -- the total output of goods and services in the economy -- rose at a 1.2 percent annual rate after adjustment for inflation, the department said. Originally, the increase was set at 1.1 percent, but in the first revision lowered to 0.6 percent.

William Cox, deputy chief economist at Commerce, also said yesterday that preliminary estimates indicate real output is falling at about an 8 percent annual rate in the current quarter. If correct -- and the figure is lower than that predicted by some private forecasters -- it would be the second worst quarterly contraction in the post-war period, surpassed only by the 9.1 percent rate of decline in the first quarter of 1975.

The first quarter estimates were revised upward on the basis of later data showing a larger build-up of inventories at the wholesale level than was at first thought. While the accumulation of stocks added to the first quarter's GNP, it spells bad news for the second and third quarters as the holders of those inventories try to cut them back to get them more in line with sharply falling sales.

Commerce also issued a revised report showing first-quarter corporate profits were higher than originally estimated. After-tax profits climbed 7.6 percent to an annual rate of $158 billion from the fourth-quarter level. The department previously estimated the increase at 5.9 percent.

Marshall, in a meeting with reporters, raised the possibility the administration might propose very modest increases in existing youth jobs programs or perhaps special federally supported efforts to aid the jobless in the hardest hit industries.

The Senate approved a resolution yesterday calling for "immediate steps" to be taken to aid the auto industry, through tax incentives, restrictions with which the industry must comply. The resolution, adopted by a 90-4 vote, makes no specific recommendations and is not binding either on Congress or the Carter administration.

Marshall said he would be "very surprised" if the administration proposed an across-the-board tax cut as an antirecession measure.

President Carter has said he will propose a tax cut to take effect sometime in 1981 but that it will be designed to encourage business investment and fight inflation, perhaps through direct or indirect cuts in Social Security payroll taxes, which are part of the cost of labor to employers.

Key administration economic officials said yesterday planning for such a cut is under way but not in a detailed fashion. They said they do not expect any announcements about a tax cut for some time, with details perhaps coming as late as January in the annual budget submission to Congress.

Treasury Secretary G. William Miller, responding to published reports the administration is considering a tax cut for next year, said President Carter "has made no decision yet on tax proposals which might be considered for implementation after 1980." Miller ruled out any tax cuts for this year.