The nation's unemployment rate jumped to 10.4 percent in October, topping the September figure that shattered a 42-year record, as the number of jobs dropped sharply and layoffs climbed further, the Labor Department reported yesterday.

There are now 11.6 million Americans out of work, with full-time adult workers particularly hard hit by the recession and a growing number of long-term unemployed, the report showed.

Democrats and union leaders issued an immediate call for swift action to relieve unemployment, which AFL-CIO President Lane Kirkland called "an economic and social disaster."

The depressed state of the economy and record unemployment levels were major factors behind the Democratic gains in Tuesday's elections, analysts say.

However, President Reagan opposes any new emergency measures, remaining confident that his present economic policies will bring down unemployment "in the near future," the White House said yesterday.

Reagan is "sympathetic and concerned about the difficulties of those who are unemployed," deputy press secretary Larry Speakes said. But administration officials see no need for any jobs program, sources say.

Democrats promised to go ahead anyway with a package of jobs measures for consideration in the lame-duck session of Congress due to start Nov. 29.

House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) last month asked the Joint Economic Committee to draft emergency legislation to bring down unemployment.

Yesterday the committee chairman, Rep. Henry S. Reuss (D-Wis.), outlined a plan that would cut defense spending to provide more federal spending on transportation, subsidies for homebuilding and new public sector jobs.

"The voters . . . want action, action now," he told reporters.

October's overall unemployment rate is the highest since 1940, the last year of the Great Depression. Post-Depression highs also were set last month for adult men, adult women, full-time workers, those aged 25 and over, and blue-collar workers. Black unemployment stayed at a record level of 20.2 percent, while white unemployment climbed from 9 percent to 9.3 percent.

In September the jobless rate climbed into double digits, at 10.1 percent, for the first time since 1940.

Unemployment could climb still higher in coming months, economists warned yesterday, because the long-awaited economic recovery has failed to materialize.

Yesterday's unemployment report shows that "the economy continued to contract last month," Otto Eckstein, head of Data Resources, said. "The recovery did not begin in October," he added, and might not do so in November.

Reagan hoped that a consumer boom would pull the economy out of recession.

But consumers have not stepped up their buying despite the income tax cut in July and recent sharp declines in interest rates.

Meanwhile, businesses are slashing their plans for new spending on plant and equipment. A McGraw-Hill survey of business intentions said this week that companies plan to cut these outlays next year by 8 percent, after allowing for inflation. Such a fall would be "mind-boggling," Eckstein said.

As the numbers thrown out of work by recession have climbed, the number of jobs available has shrunk. Last month total employment plummeted by 627,000 to 99.1 million, according to the Labor Department's survey of households, while industry reported a 263,000 drop in the number of jobs.

Since the recession's beginning in July, 1981, "employment has dropped by 1.8 million, and the proportion of the population employed, at 56.6 percent in October, has declined by almost 2 full percentage points," the department said.

The bulk of the lost jobs are in manufacturing.

The jobless rate in manufacturing rose to 14.1 percent in October, up from 13.8 percent in September and 8.6 percent a year earlier, yesterday's report said.

"Because this recession is concentrated in the goods-producing sector where nearly all jobs are full time and this sector employs a high proportion of prime age males, jobless rates for both of these groups are at record highs," Janet Norwood, commissioner of the Bureau of Labor Statistics, told members of Congress yesterday.

The jobless rate for those over 25 rose to 8.1 percent in October, while unemployment among full-time workers jumped to 10.5 percent from 10.1 percent in September.

Even more significantly, the number of full-time workers without jobs now exceeds the number of part-time jobless for the first time since these records began in 1963, Labor Department analyst Deborah Klein said. A year ago the part-time jobless rate was 2 percentage points above that for full-time workers.

More and more workers are remaining jobless for prolonged periods. The average duration of unemployment rose sharply from 16.6 weeks in September to 17.2 weeks in October. The record since World War II is 17.3 weeks, reached in 1961.

Basic jobless benefits run out after 26 weeks of unemployment. Last month 2.2 million people, or nearly one in five of the jobless, had been out of work for more than six months, the Labor report said. This was a rise of 10.5 percent from September.

"In October, 35 percent of the total unemployed had been jobless for 15 weeks or longer," Norwood said.

Unemployment remained unevenly distributed among groups and regions last month.

The jobless rate for construction workers was 23 percent, up from 22.6 percent in September. Blue-collar unemployment jumped to 15.9 percent from 15.6 percent in September; in October, 1981, it was 10.9 percent. White-collar unemployment last month was 5.1 percent, compared with 4.1 percent a year earlier.

In the 10 largest states, jobless rates last month ranged from 16.1 percent in Michigan and 13.8 percent in Ohio to 7.7 percent in Massachusetts and 8.3 percent in Texas.

Adult male unemployment rose from 9.6 percent to 9.8 percent in October, while adult female unemployment rose from 8.3 percent to a postwar record of 8.6 percent. Teenage unemployment was 24 percent.