WASHINGTON (AP) _ Beryl W. Sprinkel, a conservative economist who muted his criticism of the Federal Reserve Board to serve as President Reagan's top economic adviser, on Friday became the second high-ranking administration official to resign within a week.

Sprinkel, 63, cited ''personal reasons'' and a desire to return to the private sector. His resignation takes effect in late November.

Reagan, in a letter to Sprinkel, accepted the resignation ''with the deepest regret.'' Sprinkel, in his letter to Reagan, offered to help the president in any way he could when he returns to private life, and described his service in the administration as ''a treasured experience.''

In an interview, Sprinkel said he would return to Flossmoor, Ill., a Chicago suburb. He said he had no specific plans as yet, but hopes to be a corporate consultant, do some ''public speaking,'' writing and possibly some teaching.

Economists said they did not think Sprinkel's departure as chairman of the Council of Economic Advisers will signal any change in administration economy policy. He has held the post since April 1985.

''The history of the council under Reagan has been that Reagan has been his own chief economist,'' said Allen Sinai, chief economist for Shearson Lehman Brothers in New York. The council and its chairman ''have essentially been ignored by Reagan for years,'' he added.

David Jones, chief economist for Aubrey G. Lanston & Co. in New York, said the major influence on the administration's economic policy-making had been Treasury Secretary James A. Baker III and the Fed. ''I don't see any changes in budget policy or monetary policy coming out of this resignation,'' Jones added.

Leading candidates for Sprinkel's job include two other members of the council, Thomas Gale Moore and Michael Mussa, according to administration sources who declined to be quoted by name.

Close associates of Sprinkel, who spoke on the condition of anonymity, cited his disappointment with being passed over for the job of Federal Reserve chairman last June as a factor in his decision.

But Sprinkel said: ''I'm not leaving with sour grapes or irritation. I'm leaving with great respect for the governmental process and for President Reagan in particular.''

On Monday, Transportation Secretary Elizabeth Dole resigned to take a more active role in the presidential campaign of her husband, Senate Republican Leader Bob Dole.

Sprinkel said he told Reagan on Monday of his plans. ''He said he was very reluctant to accept my resignation, but the president respects personal reasons and he thanked me for all my hard work and support.''

White House officials said the announcement was delayed because the president wanted time to deal with Mrs. Dole's resignation.

Sprinkel had been a frequent critic of the Fed's monetary policies in his former job as assistant Treasury secretary for monetary affairs and, before that, as vice president and senior economist for the Harris Trust and Savings Bank in Chicago.

But he maintained a low profile in the White House job, ususally refusing to comment in any fashion on Fed policies.

However, Sprinkel said he plans to be more vocal as a private citizen. ''I have some knowledge, certain views, about policy and business issues and I expect to speak out on them.''

Sprinkel's tenure was a marked contrast to that of his immediate predecessor, Martin Feldstein, who often went public to assert that tax increases might be needed to trim the nation's huge budget deficit - a position squarely at odds with that of the president.

Sprinkel adhered to the view of former White House chief of staff Donald T. Regan, a close political ally, that dissent within the Cabinet not be aired in public.

''My purpose of keeping a relatively low profile in government is to maximize my influence on policy decisions,'' Sprinkel said. ''I think it is counterproductive for a chairman of the council to act in a high-profile way. It reduces leverage.''

Previously, Sprinkel built a reputation as a leading ''monetarist,'' a conservative school of economic thought which holds that even small changes in the nation's money supply can have a major bearing on the economy.

Monetarists contend an increase in the money supply, over which the Federal Reserve exercises considerable control, will produce a corresponding increase in inflation.

However, Sprinkel's brand of monetarism has been out of favor in recent years among many economists as the nation's money supply surged while inflation remained relatively tame.

His name had been mentioned as a possible successor as Fed chairman to Paul A. Volcker, who retired June 2. But Reagan gave the job to New York economic consultant Alan Greenspan, who had headed the Council of Economic Advisers in the Ford administration.

On Friday, Sprinkel called Greenspan ''an excellent choice. I'm pleased with his appointment.''

Reagan told Sprinkel, in the letter accepting the resignation, that ''you have served this administration selflessly for what will be almost seven years.''

The president praised Sprinkel's work with the Treasury, saying that in 1981, ''you helped to develop the strategy to handle the savings and loan crisis.''

Reagan recalled ''the skepticism we faced in 1981'' when he advanced the supply-side economic theory of building business growth through incentives to business, such as through tax cuts.

''You persuasively explained our philosophy through countless meetings and speeches as well as quiet diplomacy, and I have watched with pleasure as so many countries gradually have begun to change their own domestic policies in positive ways.''