Murray L. Weidenbaum, chairman of the president's Council of Economic Advisers, whose policy advice, like that of other administration economists, has often not been followed by President Reagan, has resigned.

Reagan casually mentioned the resignation, which he is expected to accept formally today, to a television reporter last night after being interviewed at a station in St. Louis.

"The president honored Weidenbaum's request with deep regret," White House deputy press secretary Larry Speakes said. "There is no policy dispute," he declared.

Asked if Reagan was satisfied with Weidenbaum's performance, Speakes said, "Sure, very much. He's worked well with the administration. He's worked well with the economic team."

Weidenbaum discussed resigning with the president about 10 days ago and asked that it not be announced until he had departed on a vacation this weekend. Presidential aides expressed bewilderment that Reagan had disclosed it in such an offhand manner.

The departure reflects Weidenbaum's "longstanding desire" to return to Washington University in St. Louis, from which he has been on leave, Speakes said.

However, over the last eight or nine months, there have been numerous sharp disagreements among members of Reagan's economic team and, on occasion, pointed personal attacks within the group.

Weidenbaum, for instance, recently emphasized his refusal to go along with attacks emanating from the Treasury on the Federal Reserve Board's independence with some highly critical comments about Undersecretary for Monetary Affairs Beryl Sprinkel.

At the same time, other officials in the economic policy area have repeatedly complained privately that Weidenbaum has not taken a vigorous enough role in shaping policy and has not been willing to convey "bad news" to the president.

Other administration sources maintain, to the contrary, that Weidenbaum has been trying for some time to persuade Reagan that the outlook was not as rosy as thought.

Ironically, the resignation, the second by a member of the three-man CEA in three weeks, comes as Reagan and other administration officials have openly begun backing away from previous forecasts of a strong, rapid recovery from the current recession.

"I think we have bottomed out," the president said yesterday. But in a distinct change in tone, he added, "The signs are kind of mixed when you bottom out in a recession. Now, I am not going to jump up and down and say, well, there is going to be a boom just around the corner."

Speakes said that the president has "several candidates" to replace Weidenbaum and "will be making a choice in the near future."

Jerry Jordan, whose resignation from the council was accepted July 1, is known to have been unhappy for most of his year with the administration about what he regarded as overly optimistic forecasts on future economic growth.

Weidenbaum usually found himself taking a policy position somewhere between those of Treasury Secretary Donald T. Regan and David A. Stockman, director of the Office of Management and Budget.

Until very recently, Regan had been highly optimistic about prospects for economic recovery, while Stockman last fall began urging the president to make significant changes in policy to reduce prospective budget deficits.

Weidenbaum, who has generally kept his disagreements about the precise course of policy from becoming public, is known to have favored greater reductions in the planned increases in defense spending than Reagan has agreed to accept in order to cut the budget deficits.

The CEA chairman is also known to have preferred more emphasis on raising revenue by increasing personal taxes rather than scaling back so large a portion of last year's business tax cut, as is called for in the tax bill backed by the administration and being debated by the Senate. Nevertheless, Weidenbaum has fully supported the general thrust of the Reagan program, much of which was shaped before he was named to the CEA.

In his letter of resignation, he told Reagan, "I believe that it is becoming clear that your economic recovery program is succeeding in shifting the balance of power from the federal government to the private sector . . .

"From the outset we have said that yours is a long-term program, unlike the quick fixes of the past. The substantial reductions in inflation is heartening evidence of the progress that has been made.

"Yet the overall condition of the economy underscores both the difficulty of carrying out fundamental changes as well as the continuing need to move ahead . . . to achieve your basic goal of restoring the economic strength of our country," Weidenbaum wrote.

Even within the CEA, there have been reports of significant disagreements on policy matters. Not long ago, the remaining member, William Niskanen, predicted that the nation's unemployment rate, 9.5 percent in June, would go above 10 percent before beginning to decline as the recovery takes hold. Weidenbaum publicly dissociated himself from that statement.

Last winter, as the fiscal 1983 budget was being shaped, Jordan said he felt that the Federal Reserve's targets for money growth, which he endorsed, would not allow the rapid economic expansion in the official administration forecast.

Jordan stood by the economic forecast for this year but, when asked about the apparent inconsistency between tight money and the rapid economic growth predicted for 1983 and beyond, he snapped, "Ask Murray."

Weidenbaum, director of the Center for the Study of American Business at Washington University before joining the administration, was assistant treasury secretary for economic policy from 1969 to 1971 in the Nixon administration.

In that job he had a major role in developing the concept of the federal government's revenue sharing program for state and local governments. He resigned to return to St. Louis just before Nixon decided to impose wage and price controls in August, 1971.

The CEA chairman has frequently joked while in Washington that high mortgage interest rates, in part a consequence of the administration's economic program, had made it impossible for him to sell his house in a St. Louis suburb.