President Carter has ordered his top economic advisers to stop talking publicly about raising interest rates to cool the economy, and has admonished them to let the independent Federal Reserve Board make the decision, and take the blame, on its own.

White House sources say Carter is displeased that a recommendation by his advisers for boosting interest rates has leaked out. They say the president intends to remain aloof on the issue, fearing that association with higher interest rates would damage what he perceives to be his populist image.

Moreover, although most leading economists say they believe that the economy is overheating and must be slowed soon, lest it worsen inflation, White House aides say Carter is not yet convinced that his economic policies need to be tightened.

One key aide said Carter had noted pointedly this week that his economic advisers often had "underestimated the vitality of the economy" in recent months. The president has criticized his economic aides several times in the past.

Carter's apparent distaste at the prospect of becoming embroiled in the interest-rate issue became evident in two forms this week:

In his news conference Tuesday, the president was optimistic about the inflation outlook, in sharp contrast to his visibly worried advisers. Carter told reporters he expected to see "a turn very shortly in the inflation rate downward."

Yesterday, Treasury Secretary W. Michael Blumenthal, who led the fight internally for administration support of higher interest rates, refused to discuss the issue during a breakfast meeting with reporters. Instead, he said repeatedly: "I have never publicly expressed myself about that."

Blumenthal also came down forcefully against one alternative recommendation policymakers have said they are considering-imposition of selective credit controls, such as cutting back the maximum repayment period for automobile loans.

The secretary ticked off a lengthly list of reasons why he said credit controls would not work, from difficulty in administering them to fears that they might hit the wrong target. Sources said later that Carter had telephoned Blumenthal personally to express his displeasures over recent leaks.

In a separate development, the Federal Reserve Board reported yesterday that the output of the nation's factories, mines and utilities surged 0.8 percent last month after two months of sluggishness, bolstering the contention that the economy is overheating. (Details, Page E9.)

Carter's cool reception on the interest-rate question appeared to rule out any White House action at least for the foreseeable future. The president's advisers had hoped to persuade him to act on the question in the next two or three weeks, but that now seems out of the question.

The developments appeared to confirm that, unlike his top economic advisers, Carter is not willing to take the risk that raising interest rates might plunge the economy into a deeper downturn later this year than economists expect.

Most of the president's economic aides had viewed the inflation problem as so serious that they were willing to risk a recession to show the economy. Blumenthal virtually said as much in a tough-sounding speech in Dallas earlier this week.

White House lieutenants yesterday confirmed that Carter's advisers had been almost unanimous in recommending that the president urge the independent Federal Reserve Board to boost interest rates sharply, just as it did in the dollar-rescue plan last November. The holdouts were Labor Secretary Ray Marshall and domestic staff chief Stuart Eizenstat.

However, it was not at all clear that the Fed would go along with such a recommendation, at least not without considerable presidential prodding. One Fed source said yesterday that there was virtually no support for imposing credit controls, and very little for boosting interest rates.

The main reason Carter's advisers had been urging him to push for higher interest rates was to send a signal to the nation that the administration was serious about the anti-inflation fight. Aides said a boost in interest rates might dampen business borrowing for new inventory building.

Yesterday, Alan Greenspan, former president Ford's economic adviser, said there was no question in his mind that the economy was overheating, and warned that, unless the current inventory-building slows, the economy could be headed for an abrupt downturn later this year.

In his meeting with reporters yesterday, Blumenthal departed sharply from the tack he used in his Dallas speech Tuesday, saying he now believes the administration's present economic policies are on track and that no further action is needed.

On Tuesday, the secretary had warned that the adminisration may have to tighten its economic policies further, saying that the nation "must take the risks entailed in maintaining and, if necessary, intensifying" its actions even if they "run the risk of recession."