President Reagan, cheered by a drop in the unemployment rate, yesterday predicted that joblessness has peaked and will not again rise to the post-Depression record of 10.8 percent that it reached in December.

"Today millions of Americans can take heart," the president said. "Unemployment has finally started down."

Reagan told reporters at an impromptu news conference that the decline from 10.8-percent unemployment in December to 10.4 percent in January is "a trend." Combined with increased auto and retail sales, he said, it indicates that the nation's economy is "on the move now." In a similar vein, he had said Tuesday that the nation's economic recovery has begun.

While expressing confidence that the nation has seen the last of 10.8-percent unemployment, Reagan added a caution:

"If you look at past recessions, you'll see that there's been a volatility to the unemployment figures. Now, that doesn't mean that they come up higher than the highest point. But, for example, there may be a month where it might level off or come up, say, a little above the 10.4 percent."

Despite increasing pressure from both Democrats and Republicans in Congress, the president showed no sign that he is ready to begin compromising on his economic policies. Apparently finding renewed political vigor in the lowered unemployment rate, he strongly reaffirmed his opposition to any congressional jobs program that would involve added expenditures in the budget.

He also stood firm against any attempt to reduce his defense budget, eliminate the last stage of his three-year tax cut or cancel indexing of incomes.

Reagan suggested that Congress is the only remaining obstacle to the success of his economic program.

"According to our own very cautious forecasts," the president said in his opening statement, "economic recovery will create more than 4.5 million new jobs by the end of 1984. If the Congress cooperates, if it holds the line on spending, we can enjoy strong, sustained growth without triggering a return to the double-digit inflation and soaring interest rates that caused unemployment to rise and nearly destroyed our economy."

Reagan said the nation's business leaders must not be given any reason to fear that the economy will suffer a relapse.

"I think the worst thing in the world we could do--and particularly with recovery started now--is to do anything that would smack of a tax increase, as those proposals to do away with the third-year tax cut and indexing would, and to take away those two parts of the economic program. And I just feel very determined about that."

Asked about Democratic charges that his budget proposals do not freeze expenses, as Reagan had pledged, but instead reduce social spending while increasing defense spending, the president, with an angry set to his jaw, said he had promised a freeze of the "overall total budget number."

"Within that, yes, there are some things that are increased," Reagan said, "given better--higher priorities . . . . But I believe that we have preserved the safety net as we've always said we would. And I think that it is about time--since there have been, in spite of all the talk and the term 'budget cuts,' there have been no budget cuts.

"Each year spending has gone up and what we have cut are the projected budgets that were left for the next five years by the previous administration," Reagan said.

The president said the administration is reviewing government construction projects to see if any can be started earlier to provide jobs. But Reagan emphasized that the proposals he is considering "wouldn't make any budget change."

Reagan said pressure from Congress for a jobs program came before members of Congress had a chance to see his budget proposals.

"I had an argument the other day with someone who was talking about the very thing that I was finally able, when I got a word in, to say it's in the budget already."

Reagan also renewed his support for increases in the defense budget despite record deficits, returning to his standard position that the United States limited defense spending in the last decade while the Soviet Union staged a massive defense buildup.

The president was asked if the administration had any plans for "humanitarian aid" to help the hungry and homeless.

Reagan replied, "We certainly are doing everything that we can in that regard. And there are programs that have been in place over the years for that very problem. Those people are automatically eligible for the programs that are in place. And we intend to continue that."

The questioner persisted: "It's nothing new at all?" Reagan answered: "No."

Later in the day, however, the Pentagon confirmed that Defense Secretary Caspar W. Weinberger asked the military services in late January to search for vacant housing on military installations that could be used for the homeless.