Vernon A. Walters, recently designated by President Reagan as ambassador to the United Nations, has agreed to accept the job even though he will not be a member of the National Security Council, White House officials said yesterday.

White House spokesman Larry Speakes praised Walters, a retired Army general, for his service and said he would be invited to NSC meetings when they involved his U.N. role.

Even though Speakes said that Walters' duties would be "exactly the same as all those who proceeded him," including immediate predecessor Jeane J. Kirkpatrick, other officials said they expect Walters to focus his energies on the United Nations rather than giving policy advice in Washington.

"There is a real preference in the administration for a strong U.N. role rather than an alternative secretary of state," a White House official said.

While Walters was agreeing to stay without the desired NSC membership, one of Reagan's longest and closest associates gave details on when he will depart the administration.

Speakes said White House deputy chief of staff Michael K. Deaver, whose decision to quit had been announced, will leave on May 15 to open a public relations firm here.

While Speakes brushed aside questions about whether Deaver could sign up clients while still at the White House, Deaver said he could not and would not solicit or accept business until he has left the government.

Deaver said his response to anyone interested in retaining him has been, "I can't talk to you until I'm out of the White House."

In another action at the White House yesterday, the president presented the Congressional Gold Medal to Margaret Truman Daniel, daughter of the late President Harry S Truman.

The private ceremony was attended by her husband, Clifton Daniel, members of the Missouri congressional delegation and Truman adviser Clark Clifford. The award was authorized by Congress last year on the 100th anniversary of Truman's birth.

The controversy over Walters' role provided brief embarrassment for the White House, administration officials acknowledged yesterday.

They said Walters met with the president on Friday and with national security affairs adviser Robert C. McFarlane on Saturday and that it became apparent to him at the latter meeting that he was not being given the NSC post he expected.

While Walters "wasn't too happy about this," officials said, they believed that he had accepted the job. But on Monday The Washington Times reported that Walters believed that he had been "betrayed" by Secretary of State George P. Shultz, who reportedly had assured him that he would have a place on the NSC.

"The president felt chagrined at this misunderstanding," an official said yesterday. He discussed the matter with McFarlane, who in turn called Walters and assured him that he would be a valued member of the administration team, the official said.

Kirkpatrick, while not a member of the NSC, was invited to most of its meetings and attended more than half of them during her U.N. tenure. An official said yesterday that he expects Walters to be invited to "many" meetings.

"The president will continue to seek Gen. Walters' counsel as U.N. ambassador, as a member of his Cabinet and as a personal adviser on national security matters," Speakes said.

Speakes also announced yesterday that Mitchell Daniels Jr., former executive director of the National Republican Senatorial Committee, will be named director of the White House office of intergovernmental affairs