Treasury Secretary Donald T. Regan said yesterday that despite a "discouraging" jump in the prime lending rate, the U.S. economy "is going to come roaring back in the late spring."

In an upbeat assessment of the economy before the National Press Club, Regan specifically predicted a recovery in the stock market and in the nation's depressed home-building industry, and said he believes that the interest-rate jump "is a temporary phenomenon that should wash out over the course of the next four to six weeks."

Moreover, he said "there is no need for the interest-rate curve to jump the minute recovery starts." Many financial analysts had expected that even if interest rates softened during the recession, they would bounce up again as soon as business activity increased. "I don't think interest rates have to jump up as much as some say. I don't see a 'crowding out' in 1982," the secretary said."

Regan cited as "a sign of progress" that interest rates had receded from their high of a year ago, when the prime rate had touched 21 1/2 percent. "It was down to 15 3/4 percent--that is, when this speech was written," he said a bit wistfully.

Most of the nation's large commercial banks, including Riggs National Bank, yesterday followed the lead of New York's Citibank, which Monday boosted the prime lending rate from l5 3/4 percent to l6 1/2 percent. However, Chase Manhattan Bank and Marine Midland Bank boosted their rates by only one-half percentage point, holding their charge to their best customers to 16 1/4 percent.

Asked how the nation could recover from recession in the face of interest rates that are over 16 percent and apparently in a rising trend, Regan responded: "That's a good question." He then added that the prime rate increase "had been brewing" over the past three months as a response to the rising short-term cost of money for the banks.

But he said history shows that interest rates "often bounce briefly higher once a recovery starts, and then they decline. I believe we'll see the same pattern this time."

The only thing that could impede recovery now would be for Congress "to renege on the tax cuts or to increase spending," Regan suggested. Some critics of the president's program have urged that Congress hold back the 1983 stage of the personal tax cut in exchange for a relaxation of a tight monetary policy.

The Treasury chief also said in his prepared remarks that there had been widespread "misinterpretation" of his recent criticism of Federal Reserve Board efforts to control the money supply.

"All I want from the Fed is enough money to buy an ever increasing amount of goods," Regan said. "In the vernacular of government, that means a slow, steady growth in money supply. I also believe that the Fed shares this view and wants to smooth out the recent erratic behavior in the money supply." In the question-and-answer period later, he added that "the reasons for the bulge in the money supply are not known at the moment, at least not at the Federal Reserve."

Fed officials have responded that high interest rates are not attributable so much to money supply fluctuations as to financial market uneasiness over the prospect of huge federal deficits.

When asked about the budget deficits, Regan said the new tax law will generate a larger pool of savings that the federal government and the private economy will be able to tap. He predicted that the national savings rate "will be 6 percent or better in the first and second quarters this year."

Asked about the possibility of a gold-backed Treasury security, Regan said he doesn't think that such an issue could raise enough money, and quipped that "we are . . . gluttons for money at this time." But he didn't close the door entirely, saying that "we don't want to do anything on gold" until the Gold Commission's report is filed next month.

Without much enthusiasm, Regan said he could endorse the administration's proposal for tax withholding on 5 percent of interest and dividends. He confided that the president didn't like the idea much, either, and Rep. Barber Conable (R-N.Y.), ranking Republican on the tax-writing Ways and Means Committee, who attended the lunch, told a reporter that the proposal wasn't going anywhere.