Declaring that this is "quite a crucial time in Washington," Treasury Secretary Donald Regan used unusually strong language yesterday in exhorting a group of Wall Street bond traders to help eliminate the investment community's psychological concerns, which he complained were keeping interest rates at abnormally high levels.

But a firming of short-term interest rates at levels higher than anticipated by money market experts earlier this week led two major Detroit banks and a smaller California institution yesterday to boost their prime lending rate to 16 1/2 percent from 16 percent--just three days after their base lending rate had been reduced.

Regan, speaking to a Public Securities Association meeting, complained that the financial markets are holding the Reagan administration "to a higher standard" than the past four administrations.

He also warned that, if business groups continue to withdraw their support for parts of the administration's economic program, they should be ready to accept the consequences. Specifically, Regan referred to the Business Roundtable, an organization of 200 major corporations, which last week recommended that the 1983 phase of tax cuts be delayed to trim steep federal deficits.

"If that is what you want, if that's what you're saying, that our tax cuts caused this huge deficit and our tax cuts are such an anathema that they must be raised, then you better be prepared for the consequences of what you are talking about," such as an increase in capital gains taxes, he asserted.

President Reagan and his administration are "puzzled" that interest rates remain so high when inflation has been cooling, he added. Regan speculated that the cause was "psychology, because of the fear" that private businesses would be forced out of the capital markets by huge federal borrowings. This won't occur because the administration's program is aimed at increasing savings and the overall pool of money for investments, he declared.

By criticizing high deficits, the business community has "the Congress spooked" and has led it to reconsider the tax cuts enacted last year, Regan added. He said the president had asked yesterday morning why interest rates are so high, but Regan declined to give his response. Noting that several economic advisers to the White House had no answers either, Regan added: "They all agreed, they don't know."

Although a reduction in the prime rate by several large banks on Monday and Tuesday was seen as the start of an industrywide trend, because of a significant decline in the banks' short-term borrowing costs at that time, developments in the credit and money markets since have indicated a reversal.

National Bank of Detroit, 21st-largest in the country, and Manufacturers National Corp. of Detroit, also among the 50 largest banks, were joined by the smaller Bank of California in boosting their prime rates yesterday.

The volatile prime generally is charged to top corporate customers for short-term borrowing and has fluctuated between 17 percent and 15 3/4 percent since last November, after falling from a record 21 1/2 percent at the end of 1980.

Tom Warren, a spokesman for National Bank of Detroit, said the prime was boosted yesterday because only a few institutions had moved down to the 16 percent level and that it couldn't be sustained by the bank's cost of money. The key federal funds rate, which banks charge each other for overnight lending of excess funds, had declined to about 13 1/2 percent by the end of last week and on Monday but was back up to 14 1/2 percent last night.

Other short-term rates also have moved higher, with large one-month certificates of deposit at major New York banks quoted last night at 14.2 percent compared with 13 3/8 percent just 24 hours earlier.

With the two Detroit banks at 16 1/2 percent, the major remaining money-center banks at 16 percent are Chase Manhattan, third-largest in the United States; Morgan Guaranty Trust Co. and Bankers Trust Co., all of New York; and First National Bank of Chicago. Riggs National and American Security of Washington also were at 16 percent yesterday, as was NCNB in Charlotte, N.C.

William Sullivan, an analyst at Bank of New York, said yesterday that many analysts had expected that a sharp, $3 billion decline in the money supply last week would be followed by a moderation in the federal funds rate. "But just the opposite has happened, they've short-term rates been progressively firmer as the week progressed," he said in a telephone interview.

"The psychology of the money markets--and don't ask me why--is very negative, it's worsened dramatically . . . the Federal Reserve remains committed to its monetary policy and won't accommodate the markets at this time" by easing its credit-restraint policy, Sullivan emphasized.

He also said many money-market experts expect an increase in the money supply to show up again in the latest weekly figures to be released today. Other analysts said the increase could be as high as $3 billion.

Regan argued yesterday that it was congressional failure to cut spending last year rather than tax cuts that have caused projected federal deficits to soar, causing fears about the availability of credit.

In a separate speech last night in New York, Regan sent another message to the business community: "Now is the time for business leaders to show strength, not timidity; statesmanship, not parochial interests."