Federal Reserve Vice Chairman Preston Martin submitted his resignation yesterday after failing to win White House assurance that he would be appointed to succeed Chairman Paul A. Volcker next year.

Martin, whose four-year term as vice chairman expires at the end of the month, told a news conference he is leaving for personal reasons, including an unwillingness to commit himself to remain at the Fed for another four years.

The resignation followed an attempt by Martin and three other Reagan administration appointees to force a reduction in a key interest rate over the objection of Volcker. Martin's departure leaves the board more evenly divided over whether an easier monetary policy is needed to keep the three-year-old economic expansion moving ahead strongly.

A senior White House official said yesterday that "someone of a similar persuasion" would be nominated as soon as possible to fill Martin's unexpired term on the seven-member board, which still has 10 years to run. Board members are nominated separately for the positions of chairman and vice chairman by the president and must be confirmed by the Senate.

The senior official said that White House Chief of Staff Donald T. Regan had offered Martin reappointment as vice chairman, but that "nobody was willing to give him any promises" about whether he would succeed Volcker when Volcker's term as chairman expires in August 1987. Martin was passed over for the chairmanship in 1983 when Reagan nominated Volcker to a second term as chairman. Volcker was appointed initially by President Carter.

The White House staff recognized that Martin might choose to resign if he were not promised the chairmanship, the official said.

The White House was willing to promise only that Martin would be publicly considered "a leading candidate" for the job, the official said. However, another "leading candidate" also would be Beryl Sprinkel, chairman of the Council of Economic Advisers, who is said to be Regan's choice, according to another administration source.

Sprinkel is not regarded as a candidate for the new vacancy on the board. However, some analysts speculated that he might accept the vice chairmanship if he received assurances that he would succeed Volcker as chairman.

Barring such a development, Martin, by his resignation, has not necessarily taken himself out of the running for the top Fed job, the senior White House official said.

The president may nominate a new person for both the vacancy and the vice chairmanship, or he may name one of his current appointees, Governors Martha Seger, Manuel Johnson and Wayne Angell, as vice chairman.

Another board member, Henry Wallich, recently had major surgery. He is back at work, but is recovering slowly, according to Federal Reserve sources. Should he decide to retire, the president would have a chance to make another appointment.

In what some close observers of the Federal Reserve regarded as an attempt to force Volcker to resign, Martin led a surprise attempt to force a cut in the central bank's discount rate over the chairman's strenuous objections on the morning of Feb. 24. Martin, Seger, Johnson and Angell, all named to the board by the president, initially prevailed in a 4-to-3 vote.

But about 3:30 that afternoon, an hour before the decision was to be announced, one of the four, Angell, changed his mind. The board met again and rescinded the first vote. Volcker had opposed the reduction out of a fear that a cut in U.S. interest rates might cause the dollar to plunge on foreign exchange markets, with serious inflationary consequences to follow.

Volcker was so disturbed by the vote that he considered resigning before the rate cut was put off. Ten days later, after central banks in West Germany and Japan made similar cuts, the Fed board voted 6 to 0 to cut the discount rate from 7 1/2 to 7 percent.

At his press conference yesterday, Martin, 62, said he thought on Feb. 24 that "it was appropriate to go forward with a discount-rate reduction then because I had reason to believe that there would be other countries joining us."

Martin, a Californian who served in Reagan's state administration there and later as chairman of the Federal Home Loan Bank Board, which regulates most savings and loan associations, said that he plans to return to San Francisco and to the private sector. "We are all aware that the financial world offers a number of opportunities these days," he said.

The vice chairman turned aside all questions about whether he wanted to succeed Volcker, saying that there is "no vacancy in the chairmanship."

Asked if he was tired of serving on the board, Martin declared, "No, I am not tired of being on the Fed. This is one of the most exciting crisis-management centers on the planet. But my term is up."

After the announcement, Volcker issued a statement saying, "Mr. Martin has brought a wide experience and background in public and private life to the nation and to the Federal Reserve. He is a man of strong and independent views as befits the board. He has played a leadership role in many aspects of the system's work, bringing to bear his special insights into financial institutions, the financial system and markets, and carrying particular responsibility for relationships with the reserve banks. . . . "