The nation's unemployment rate edged up a fraction to 10.8 percent in December, and the White House confirmed that it expects only slow growth in the economy during 1983. Sources said this slow growth would leave unemployment still well above 10 percent at year-end.

The December jobless rate was the highest since the end of the Great Depression, although it matched the figure originally reported for November by the Labor Department a month ago. The department yesterday issued a revised figure of 10.7 percent for November.

The slight rise in unemployment last month, together with a slowdown in factory job losses, indicated that the worst of the recession-induced rise in unemployment may be over, officials said.

The White House said it expects the economy to grow by only 3 percent this year, after accounting for inflation. This growth rate between the end of 1982 and the end of 1983 will leave real Gross National Product for 1983 just 1.4 percent higher than the average level last year, deputy press secretary Larry Speakes said yesterday.

The administration's forecast for unemployment is due to be released officially Jan. 31, when the 1984 budget is to be published.

The latest economic forecast from the Congressional Budget Office shows slightly stronger growth during 1983 than the administration predicts, with unemployment still as high as 10.5 percent by the end of this year, a source said yesterday.

It would not be surprising if the administration forecast also showed a jobless rate close to 10.5 percent by year-end, sources said. Slow recovery in the economy will keep unemployment above 9 percent through 1984, according to unpublished administration forecasts, sources said.

The administration's latest economic forecast is more gloomy than that of many private analysts. Previous White House projections were strongly criticized for being over-optimistic and President Reagan's new economic adviser, Martin Feldstein, was particularly keen to produce a realistic set of projections to accompany this year's budget documents, sources say.

The recovery the administration projects would be the slowest of any since World War II and comes on top of the most severe recession since then.

The jobless rate for 1982 averaged 9.7 percent, the worst since the 9.9 percent rate recorded for 1941, yesterday's Labor Department release said.

In addition to the 12 million counted among the officially unemployed in December, there were a record 1.8 million people who wanted a job but had given up looking for work in the final quarter of the year, the Labor report said.

Although yesterday's jobless numbers suggest a leveling-off of recent sharp rises in unemployment, the labor market remains bleak, analysts said.

The jobless rates for adult men, adult women, blacks and teen-agers hit new post-World War II highs in December, and the average length of time spent out of work rose to a postwar record of 18 weeks, the Labor Department said.

Black unemployment totaled 20.8 percent last month, compared with a jobless rate for whites of 9.7 percent.

The White House said that the new release "indicates to us that unemployment is still too high." But, Speakes added, "It did not rise exceptionally this month and we believe it will come down in the coming months." Speakes said that the economy was entering a "period of sustained growth."

The White House forecasts for the economy, on which the fiscal 1984 budget numbers will be based, predict real GNP growth of 1 percent in the current quarter of 1983, 3 percent in the second quarter and 4 percent in the third and fourth quarters, Speakes said.

In the early stages of previous recoveries the economy has grown at an annual rate as high as 6 or 7 percent, or more. The White House assumes 4 percent annual growth for the years 1984 through 1988, the end of the forecasting period, Speakes said.

Democrats criticized Reagan for the jobless total, and called for new jobs programs to combat unemployment.

House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) said, "The time for action by the federal government to end this depression is now. I call on the president to drop his opposition to a jobs bill."

The number of factory jobs continued to decline last month, but the "composition and nature" of the 165,000-job drop was "quite different from the job losses of previous months," Janet Norwood, commissioner of the Bureau of Labor Statistics, told members of Congress.

"Factory employment losses were smaller and not so widespread as in recent months," she said, while "the largest decline . . . in December was in retail trade."

Retailers hired fewer workers than usual during the Christmas period so that, after seasonal adjustment, a 65,000 decrease in retail employment was recorded in December.

Total employment edged down by 43,000 to 99.1 million in December, the release said. This was little changed from the October and November totals.