President Reagan made an extraordinary plea yesterday for each business in America to hire "just one person" from the ranks of the jobless, even though he predicted that 1983 would bring "a definite upturn" from the worst unemployment since the Great Depression.

"I know that there are some businesses that, themselves, are faced with troubles and cannot do this," the president said. "But if a lot of businesses would take a look and see if they could hire just one person, it would be interesting to see how much we can reduce those unemployment rolls."

"There must be some that cannot, I know, because of their own troubles," Reagan added, "but there must be others that could probably do even more than one . . . . If everyone would just simply look at it from the standpoint that there are more businesses in the United States than there are unemployed."

The president's suggestion came in a 15-minute question-and-answer session with reporters in the White House briefing room at which Reagan also lavished praise on the just-concluded lame-duck session of Congress and described his Sept. 1 Mideast peace initiative as his "greatest accomplishment" in 1982.

Reagan was questioned repeatedly about the difficulties the administration has encountered with mushrooming federal deficits and the highest unemployment rate since 1941.

The president, who convinced Congress to drop a public works jobs program from the catch-all spending bill he signed this week, said he is "convinced that this coming year, 1983, is going to see a definite upturn" in the employment situation. The national unemployment rate is 10.8 percent, with about 12 million people out of work.

"I wish that I could promise that unemployment would instantly respond," the president said. "But we know from seven previous experiences since World War II that it does not. It is the slowest thing in recovery."

After taking note of what he called the "neighborly spirit in America" to cope with hard times, Reagan said he wanted to "suggest to the whole business community" that if each firm hired one person it might reduce the jobless rate.

He did not elaborate, but White House counselor Edwin Meese III told reporters later in the day that the president's suggestion would "certainly make a real dent" in the unemployment situation.

He said Reagan picked up the idea from the Rev. Leon Sullivan of Philadelphia, who has developed a network of job-training centers for the poor and marginally employable.

Questioned about how businesses could be convinced to hire more people when many of them have been laying off workers, Meese acknowledged that some industries have been "particularly hard hit by structural and cyclical events."

But, he added, "We're talking about the general run of businesses. And if each business can figure out, this may really involve in some cases not letting someone go that they might have to, by staggering work hours or something like that, that's what the president is talking about."

Reagan has largely refrained from directly jawboning American business.

He once lamented the poor performance of the stock market after his tax cut was passed in 1981, but a central premise of the administration's philosophy has been that in the "magic of the marketplace," to use Reagan's words, business would automatically respond positively to the tax cuts and other investment incentives offered by his administration.

The president's contention that there are more businesses in the United States than unemployed workers is not easily verified because many businesses exist only on paper, while others are part of massive conglomerates.

A spokesman for the U.S. Census Bureau said yesterday that, based on tax returns, there are 4.8 million firms in the nation. But he noted that many firms may file only one return.

Other estimates put the number of American businesses as high as 14 million, according to the 1981 edition of the Statistical Abstract of the United States.

Regardless of whether the numbers match, many economists have pointed out that it is more difficult to solve the unemployment problem than simply having each firm hire one person.

Jerry J. Jasinowski, chief economist of the National Association of Manufacturers, said yesterday there is "not a very neat match" between the people needing work and the number of businesses.

"The bulk of unemployment is in heavy industry," he noted, while small firms have not experienced such massive layoffs. "Hundreds of thousands are in manufacturing industries, so the bulk of unemployment occurs in a limited number of firms, in selected industries."

When questioned about the job creation proposals he threatened to veto, Reagan recalled how his father held a government job in the Depression, in which he and another official were in charge of federal relief for the poor.

According to Reagan's account, which also appears in his autobiography, "Where's the Rest of Me?", his father voluntarily and "single-handedly" organized an effort to match jobless workers with employment that was available in Dixon, Ill.

Reagan said the federal government then intervened and "figured it out that they couldn't take that work" because the workers would then be denied "relief" and would have to reapply for it. "And that took longer than the amount of work that they'd had. So, they were forced onto permanent relief. They couldn't work."

The president said his father "had the common sense that he would know that temporary fixes wouldn't work."

Reagan also yesterday refused to directly criticize the GOP senators who filibustered the nickel-a-gallon gasoline tax increase and helped kill his Caribbean Basin initiative for the year. "I have been dealing with legislators for 10 years," he said, "and so I am not too surprised by things that happen . . . . They have their own rules."

The president did suggest the need for "reform" in the federal budget process, but he did not offer any remedies other than spending bills should be completed by the beginning of the fiscal year.

Questioned about the federal deficit, Reagan said the "greatest single factor" is the recession and the fact that "you have millions of people who are not paying taxes who normally do."

On foreign affairs, Reagan said the administration has made "great progress" in dealing with its allies and with nations in the Western Hemisphere. But he said his "greatest accomplishment" was his Middle East initiative, launched in a speech Sept. 1.