The nation's unemployment rate jumped to 10.1 percent in September, the highest jobless rate since 1940, with adult men particularly hard hit by persistent deep recession and rising joblessness, the Labor Department reported yesterday.

Democrats and labor leaders seized on the unemployment numbers as evidence of the failure of President Reagan's economic policies, calling the September figures a national tragedy. Reagan administration officials sought to blame their predecessors for the state of the economy, and held out hopes of a recovery ahead. And Reagan pointed to a tremendous rally in stocks and bonds this week as evidence that the economy will pick up.

In its last monthly unemployment rate release before the Nov. 2 congressional midterm elections, the Labor Department said that 11.3 million Americans were out of work in September, up by 450,000 from August, as layoffs increased and the number of factory jobs dropped. Black unemployment hit a new record of 20.2 percent, highest since the end of World War II, when this figure was first reported.

The release of the new unemployment figures was accompanied by action by the Federal Reserve yesterday afternoon to lower a key interest rate, amid reports that the Fed has decided privately on a major policy shift to help revive the economy by making credit more available and pushing interest rates lower.

After stock markets closed yesterday, the Fed lowered its discount rate from 10 to 9 1/2 percent, thus making it cheaper for banks to borrow from the Fed, and while there was no confirmation yesterday of a new policy, the financial markets continued to give evidence that a shift has occurred.

Stocks soared yesterday with the Dow Jones Industrial Average climbing nearly 20 points to 986.85, the highest level in 15 months. More than 123 million shares were traded on the New York Stock Exchange, the fifth heaviest buying activity on record. Bond prices also climbed as market interest rates fell sharply.

The market rallied despite continuing evidence of a very weak economy which many private analysts expect to stay depressed for at least the balance of this year.

Presidential economic adviser Martin S. Feldstein warned yesterday that unemployment could edge higher. "Nobody likes that kind of unemployment. I think that if we have a moderate recovery we will get improvement in the unemployment picture, but we will not get a dramatic improvement," Feldstein said at a meeting of business executives in Hot Springs, Va.

Treasury Secretary Donald T. Regan told reporters yesterday the administration is "sticking to" Reagan's economic program, which he said had brought down inflation and interest rates and set the stage for recovery.

"We reject the quick fixes of the past," Regan said, adding, "I want to reassure the American people that we are on the right track, that we will not go back to the policies of the past."

But House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) said he would schedule immediate House action on "needed recovery measures" when Congress reconvenes for a lame-duck session Reagan has requested late in November. "The situation demands that Congress move directly to restore public confidence and regain control of the nation's economic destiny," O'Neill said.

"I am angry," said Rep. Parren J. Mitchell (D-Md.) at a hearing on the unemployment figures yesterday, criticizing Reagan as "this dreadful man."

"These tragic figures reflect the terrible price of Reaganomics," AFL-CIO President Lane Kirkland said.

Regan yesterday said the nation was "in that recovery stage . . . . We see a recovery coming." But this week the Federal Reserve, which is reponsible for monetary policy, was presented with a pessimistic staff assessment of the economy, sources said, and decided on the basis of this forecast and the evidence of increasing strains in the nation's banking system to ease up on credit and bring interest rates down.

This policy shift could lead to the revival in the economy which has so far stubbornly refused to materialize, private economists said. High interest rates and the Fed's tight monetary policy have been a major factor holding the economy in recession, they believe.

Regan refused to blame the Fed for high unemployment, and when asked whether the administration is to blame said, "I don't think that's a game I want to play, who's responsible for what." Feldstein said earlier that high unemployment is the price paid for reducing inflation, and Regan has agreed there is a trade-off between unemployment and inflation, at least in the near term.

Fed Chairman Paul A. Volcker is scheduled to speak at the business executives meeting in Hot Springs today. At this point, there has been no word from the Fed of a policy shift, and Feldstein said, "I think the Fed is continuing its basic policy of controlling the rate of growth of the money supply."

The September unemployment report showed that on top of the 11.3 million who reported themselves as out of work, a record 6.6 million Americans were forced to work part-time last month because they could not find a full-time job. In addition, new quarterly figures showed a rise in the number of people who wanted to work but did not report themselves as unemployed because they did not think they could find work to a new record of 1.6 million in the three months to September.

Unemployment has climbed 2.9 percentage points since July, 1981, when the recession began. Although all sectors of the labor force have been hurt by the recession, adult males have been hit particularly hard, Bureau of Labor Statistics Commissioner Janet Norwood said yesterday.

"Since the recession began in 1981, the unemployment rate for black men has climbed from 12.7 percent to 19.8 percent and the rate for white men has risen from 5.0 percent to 8.6 percent," Norwood said.

The over-25 age group, which typically has lower-than-average unemployment, also suffered a sharp rise in joblessness. Last month the unemployment rate among these workers jumped from 7.3 to 7.9 percent. A year ago this rate was below 5.5 percent.

Manufacturing has been particularly hard hit by the recession, with durables industries such as autos especially affected by high interest rates that have characterized the downturn.

There was a further decline in jobs in manufacturing last month, Norwood said, bringing to 1.8 million the total job loss in this sector since the recession began.

The factory work week fell by 0.4 of an hour in September, the second monthly decline in a row, yesterday's report said.

Industry's weakness has pushed up the unemployment rate for blue-collar workers. This jumped by 1.4 percentage points to 15.6 percent last month, the Labor Department said. White-collar unemployment was 4.8 percent.

The jobless rates for adult women rose slightly from 8.2 to 8.3 percent while that for teen-agers slipped from 24 to 23.7 percent, the report said.

Reagan had hoped that consumers would pull the economy out of recession by spending the tax cuts that went into effect last July. However, as sales have continued to slide stores have apparently scaled back their hopes for a fall recovery.

"In September, retail trade employment declined by 45,000 as retail stores failed to hire the usual number of workers in anticipation of the pick-up in fall and winter sales," Norwood said.

Services, which employ about three out of every four workers, are generally less affected by recession, she said. They have lost about 190,000 jobs since July, 1981, the Bureau of Labor Statistics reported.