President Reagan, sounding the themes of the Republican campaign that Americans should stick to his economic course, declared last night that he has made progress on all major fronts except unemployment and that his policies also are "getting to the roots" of that problem.

Less than three weeks before the Nov. 2 congressional elections, the president closed what was billed as a nonpartisan "progress report" on the economy by repeating the Republican campaign slogan that Americans can return to prosperity "by staying the course" he has set in the last 21 months.

In a nationally televised address that borrowed heavily from his political speeches so far during the campaign, Reagan told the nation that his administration has "made important progress" on "four out of five problems that faced us in 1980. We have not solved them all, but we are making headway."

Saying that "America is recovery bound and the world knows it," the president pointed to gains in fighting inflation, bringing down interest rates, reducing federal spending and trimming tax rates. "All of this lays the groundwork for a recovery that will mean more jobs and more opportunity for all our people," he said. "But it is a delayed reaction."

Following the president's appeal to Americans not to abandon his program, Sen. Donald W. Riegle Jr. of Michigan presented the Democratic response. "The course needs to change," he said. "The truth is that this administration has created two courses -- one of them a very fast economic track for a few, the other filled with potholes and roadblocks for the rest of us."

"More people are out of work now than at any time since the Great Depression," Riegle said, "and it's getting worse . . . . And we're supposed to stay on this course? Unemployment is worse; business failures are worse; farm failures are worse; the economy is steadily grinding down the middle class."

The Oval Office speech and Riegle's response last night came as the congressional campaigns go into the final stretch, with Reagan's economic program the center of increasingly partisan debate.

One television network, ABC, refused a White House request to provide free air time for the president's speech on grounds he was delivering a partisan appeal for GOP support; CBS and NBC did broadcast the speech.

The Democrats complained that they were short-changed in the time allotted for their response, and Riegle pointed out that he had to abridge his comments because the president left him only five minutes before the start of the second World Series game on one of the networks.

With the nation's jobless rate above 10 percent, the president acknowledged early in his address that unemployment "is the problem uppermost on many people's minds."

But he then sought to make a case that his policies, instead of causing the increase in unemployment, were designed to bring the jobless rate down. " . . . Remember, you can't solve unemployment without solving the things that caused it -- the out-of-control government spending, the skyrocketing inflation and interest rates that led to unemployment in the first place," he said.

"Unless you get at the root causes of the problem -- which is exactly what our economic program is doing -- you may be able to temporarily relieve the symptoms, but you'll never cure the disease. You may even make it worse."

The president cast unemployment as an economic malady that has been building for decades, the result of a "pounding economic hangover" that "didn't come about overnight, and there is no single, instant cure." Pointing to a graph of unemployment that had no annual dates or figures on it, Reagan said it was a reminder that "the current recession is part of a long series -- a series that hasn't stopped because, in the past, when the crunch came, too many in government resorted to quick fixes instead of getting to the root cause."

The president's 23-minute speech again demonstrated the White House strategy this fall of attempting to make a virtue out of Reagan's greatest economic liability -- rising unemployment. Thus, he maintained last night that his plan to tackle inflation was the right one because inflation was the "culprit" behind unemployment.

"Each time inflation has shot up since 1969," Reagan said, "there has been a deadly, delayed reaction of rising unemployment."

Fighting that unemployment with a "quick fix" was unsuccessful in the past, the president added, and the result was "those twin disaster lines kept inching ominously upward, bringing our society closer and closer to catastrophe."

"Well, at my age, I did not come to Washington to play politics as usual," the president said, vowing to reject the economic strategies of the past. He said the program now in place confronts the nation's economic ills "and has already started solving them."

"Getting to the roots of unemployment meant fighting inflation and high interest rates caused by runaway government spending and taxing," Reagan said, promising that because "inflation is being driven back down, lower unemployment will follow."

"I wish there were a quicker, easier way -- some magic shortcut -- but unemployment is always one of the last things to turn around as the economy heads into recovery," he said.

Taking note again of the climbing stock market, the president said it reflected a "decision to put cash on the line" in "a strong vote of confidence in the foundation being laid for America's recovery . . . . " Although he claimed that this vote of confidence was coming from "small investors on Main Street," among others, Wall Street brokers have been saying in recent days that most of the market activity is from large institutional investors.

Missing from the president's review of the success he has scored in turning around the economy was any mention of investment in new plants and equipment, which has not expanded as the original Reagan program had optimistically projected it would.

But Reagan attempted to reach out to voters who, according to public opinion surveys, have been feeling helpless in the economic turmoil of recent months. He quoted from a letter sent to him "from a wife and mother named Judith" in Selma, Ala., who demanded: "We must know that in the tons of bureaucracy we have not been lost. . . . We feel so out of control. We don't want a handout, we just want to help make the system well again."

"Judith, I hear you," Reagan responded.

After recounting the four major economic problems he has tackled--inflation, government spending, taxes and interest rates -- the president laid out what he hopes will be the agenda for the post-election lame-duck session of Congress. It should include, he said, 11 remaining appropriations bills, reconsideration of the balanced budget constitutional amendment, action on regulatory reform, passage of his enterprise zones for blighted urban areas, and approval of the revised Clean Air Act.

And Reagan closed with what essentially has been his appeal to voters this year. He rejected the "taxing and taxing" policies of the past as "no alternative," saying that prosperity can only br brought back "by staying the course."

In response, congressional Democrats branded the president's course a failure. "If he thinks Reaganomics is working, he should talk to the fella who isn't," said House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.).

Rep. Henry S. Reuss (D-Wis.), chairman of the congressional Joint Economic Committee, said Reagan had offered "an eloquent apology for the failure of his economic policies."

Democratic National Chairman Charles T. Manatt said earlier yesterday that his party would pursue action before the Federal Communications Commission against NBC and CBS television networks because they did not give Riegle equal time to respond to Reagan. The senator was alloted just a few minutes on NBC and CBS planned to produce their own half-hour Democratic response later in the evening.

The partisan jostling over the economy came on the same day that Reagan signed a job training bill amid continued squabbling with Democrats over who should take credit for it just 20 days before the voters go to the polls.

Last night, Riegle, speaking for Democrats, challenged Reagan's claims that the stock market was rebounding as a vote of confidence in the administration. "Are we to believe that a stock market boom means we are on the road to recovery?" he asked. "The market boomed the very day that unemployment passed 10 percent for the first time since the Depression. The stock market also boomed in 1929 -- just before the Depression."

"We are all glad to see Wall Street rally," he added, "But the problem, though, is on Main Street. And on Main Street, the numbers are still heading down."