President Reagan sought yesterday to smooth over the most public and embarrassing dispute of his administration by reassuring his unhappy secretary of state, Alexander M. Haig Jr., that he remains the president's principal former policy adviser.

After failing Tuesday in an effort to take control of foreign crisis management, Haig went to the White Hosue yesterday morning upset and close to offering his resignation, according to sources with access to him.

Reagan told reporters later that Haig did not actually threaten to resign during the 45 minutes he spent at the White House. "No.He never once threatened," Reagan said.

According to White House officials, however, Haig did speak of resigning to senior White House aides. A State Department source also said Haig gave the impression to subordinates before his 9:15 a.m. meeting with Reagan that he was prepared to resign.

Despite efforts by Reagan and Haig spokesman William Dyess to portray the dispute as ended, there were reports that the secretary of state was not entirely satisfied with the outcome. At the White House and State Department there was continuing concern about the future of the working relationships between Haig and senior presidential advisers and a sense that much remains unresolved.

Showing no concern over the controversy, Reagan, in jodhpurs and brown boots with spurs, stopped on his way to an afternoon of horseback riding to read a one-paragraph statement to reporters and television camera crews.

He spoke against the background roar of a Marine helicopter poised on the White House South Lawn to fly him to the Marine base at Quantico, Va., where he planned to ride a 15-year-old mare named Bonus. Nancy Reagan watched the scene half-hidden by a column on the second-floor Truman Balcony.

The president's determination not to break his pattern of taking Wednesday afternoons off as a midweek break underlined his effort to close the book on the dispute that began Tuesday when Haig publicly expressed dissatisfaction with policy-making procedures and specifically questioned the idea of giving Vice President Bush control of government action during periods of crisis.

Hours after Haig made his critical remarks to a House subcommittee, Reagan formally decided and announced that crisis managment will be headed by Bush, not Haig.

Reagan's statement yesterday did not address the core of the dispute, but stressed his reliance on Haig.

"One of the principal responsibilities of a president, as we all know, is the conduct of foreign policy. In meeting this responsibility, let me say what I said a number of times before. The secretary of state is my primary adviser on foreign affairs and in that capacity he is the chief formulator and spokesman for foreign policy for this administration. There is not, nor has there ever been, any question about this."

The president was asked what he thought of the Haig testimony that triggered the chain of events. Haig told a House subcommittee Tuesday that he had read with "a lack of enthusiasm" newspaper reports that Bush would head crisis management.

"I don't think a decision has been made on this issue; at least it has not been discussed with me if one has been made," Haig said. If a decision had been made without his knowledge, he added, "that would pose another set of problems."

"I don't know if you will like my reaction," Reagan told reporters when asked about those remarks.

"My reaction was that maybe some of you were trying to make the news instead of reporting it."

White House press secretary James S. Brady, however, said later that he does not think the dispute was manufactured by reporters.

The upshot of the events of the past two days was to weaken Haig's prestige and authority in the public arena and within the inner circles of the administration. This was not the first time that the assertive former general tangled with the senior White House staff, but it was by far the most dramatic, public and most damaging.

It also was not the first time Haig has talked of resigning. White House sources said the volatile secretary of state mentioned resigning during earlier controversies.

Despite the flurry of public denials that Haig had "threatened" to resign yesterday, the length of the secretary of state's tenure in office was clouded and uncertain.

As late as midafternoon yesterday, hours after the Reagan-Haig meeting and the president's public statement, a source close to Haig reported the secretary of state to be still nervous and upset and said there remained a substantial chance, perhaps 30 percent or so, that he would not stay in office.

After Reagan's decision giving control of foreign and domestic crisis management to Bush was announced about 6:15 p.m. Tuesday, Haig convened his closest advisers at the State Department for a meeting that did not break up until well after 9 p.m. Haig was described as fed up with the internal criticism, which he felt was aimed at him, over the division of policy functions.

He left the meeting, according to sources, with his future in the balance. Unless the president made it clear that Haig would have the authority he felt he needed for the conduct of foreign relations, the secretary of state was determined to step down.

Specifically, the sources said, he wanted a presidential statement of his authority. One official suggested that Haig still had not given up all hope of reversing the already announced decision on crisis management.

Haig did not appear in public after his meeting with Reagan yesterday morning. His spokesman told reporters: "To the best of my understanding, following his conversations with the president, he is satisfied."

Other officials, however, said that the president's statement had not been all that Haig had hoped for. And it seemed clear that the crisis management role was firmly in the hands of Bush and the National Security Council staff.

Moreover, the dimensions of that role did not seem limited by anything said in public yesterday.

Bush was asked what constitutes a crisis and replied: "We'll know it when the president sees it. . . . We're not talking about day-to-day situations like we have today in Poland or El Salvador -- absolutely not." He added, "Even I think it will all work out."

The president remains the chief crisis manager, Bush and others pointed out. The dispute is over who will act for Reagan in his absence. "I will be in charge of the situation room when the president cannot get there," Bush said.

Haig and Bush both have had presidential ambitions. Haig tested the waters but found them chilly in the race for the 1980 Republican presidential nomination. Bush was the last candidate still opposing Reagan before the president wrapped up that nomination.

Reagan is 70 and thus a second term is in doubt although his aides report he will run if he feels as healthy in 1984 as he does now. Bush and Haig could find themselves competing to succeed Reagan should the president choose not to seek a second term. In the view of some observers, the struggle over crisis management has some of its roots in presidential politics.

Haig, after saying nothing in public yesterday, is scheduled to return to Capitol Hill this morning to appear before the Senate Appropriations subcommittee on foreign operations. The subject is the State Department budget, the same topic Haig was addressing Tuesday when congressmen questioned the degree of his satisfaction with his place in policy making.