Some of Walter E. Washington's old friends and some of his political rivals have been trying since March to get the mayor out of city hall andinto an American embassy in some foreign country.

The group is led by Del. Walter E. Fauntroy (D-D.C.), and Robert B. Washing Jr., chairman of the D.C. Democratic State Committee.

Fauntroy has talked with Secretary of State Cyrus R. Vance. The group has gotten advise from Sol. M. Linowitz, cochairman of the U.S. team negotiating a new Penama Canal treaty. Sen. Hubert H. Humphrey (D-Minn.) has sent in a letter of recommendation. But so far, according to well-placed State Department sources, the mayor's name has not been seriously considered for any diplomatic post.

Both Fauntroy and Democratic chairman Washington are political allies of City Council Chairman Sterling Tucker, who is considered by some to be a principal threat to the mayor if the mayor should seek re-election in 1978. Tucker himself was not directly involved in the effort, sources said, though he has received "a few reports ont he status of things from time to time."

A spokesman for the mayor said the mayor was at home "on leave and his office is reaching him only on matters that require his attention." This one did not, said Sam Eastman, the mayor's press secretary.

Fauntroy was the only one of the participants willing to discuss the effort for the record.

Fauntroy insists that this effort, which has not been sanctioned by the mayor, is not politically motivated. He and others contend that it is not important that the mayor's departure from office before the end of his term would make Tucker the temporary head of city government and, in the view of some observers, virtually assure Tucker's election as the city's next mayor.

Those involved say theirs is a compassionate campaign of civic concern that is best not only for Washington the city, but also best for Washington the man, who has been mayor of the nation's capital for the last 10 years.

"I don't intend to support the mayor for re-election in 1978," Fauntroy says. "If he runs, he will be defeated. I think the mayor deserves more than that kind of exit. I would prefer to see the mayor make the transition in an orderly fashion."

=Everybody believes that Walter Washington has given the (mayor's) job his best and that if the's going to be in public service, this (ambassadorship) is the kind of assignment at which he will do best because it appeals to him most - the pomp, the circumstance and the perks (perquisites of office)," said another source who knows about the effort.

Another key participant summed it up this way: "Whatever one may think of his administrative ability to run a city, he is capable of running a foreign mission and participating in our foreign policy. It would be a plus for the city because we would have a more competent person at the helm of the city. What that person would be is not a function of our action."

Ever since Jimmy Carter's election last year as the first Democratic president in eight years, there has been speculation in local political circles that the mayor might receive a top-level appointment in the new administration.

The effort by Fauntroy and Democratic chairman Washington appears to be the first clear evidence of an attempt to secure such an appointment. It is also, in some respects, a story of Washington, the city, beginning to come of age politically, involving some of the most notable emerging power brokers in the city's recently reborn political process.

Fauntroy said the drive began in March, shortly after the end of a two-day takeover of three buildings in the city by 12 armed Hanafi Muslims. The mayor, working with three Islamic ambassadors, had helped secure the release of 134 hostages held by the Muslims.

"I felt that he had handled the crisis impressively enough to warrant consideration for one of the diplomatic post," Fauntroy recalled in a recent interview. "He has great assets best used in the kind of diplomacy he displayed in working with foreign ambassadors in handling that very delicate situation."

There were also other factors involved, however, according to knowledgeable sources. The mayor, at that point, was in the fourth month of a political crisis centering on allegations of mismanagement and possible bribery involving his longtime political ally Joseph P. Yeldell, then director fo the D.C. Department of Human Resources.

"The way the mayor was handling the Yeldell situation seemed to suggest that he was commiting political suicide," one source familiar with the appointment effort said. "There might not have been any opportunity later. The mayor might have been forced out or driven into retirement."

Time appeared to be an important consideration. The President's advisory board had already begun considering more than 700 persons for 30 ambassadorial posts in the first large group of diplomatic appointments that the administration would make.

It was important, Fauntroy said, to get reaction to the mayor's possible selection from someone who was familiar with the requirements for diplomatic service. So he and Democratic chairman Washington arranged a meeting with LInowitz, former U.S. Ambassador to the Organization of American States and a longtime friend of Vance, who had already been confirmed as secretary of state.

Linowitz, in whose law office the meeting was held, asked Fauntroy and Washington if the mayor had sbeen talked to about the effort and was told that the mayor had not, sources said.

"The mayor has been serving all this time, he's kind of tired," one source said Linowitz was told. "Bennetta (the mayor's wife) would love it, too. He won't admit it, but he would probably like it himself."

Fauntroy later recalled that "it never occurred" to him to ask the mayor. "I had been through a period of recommending a number of people for a number of positions and I just hadnt been checking with the principals. I had understood that the mayor would be interested in an appointment if a suitable one were offered him."

Another key participant said that the mayor was believed to feel that it would be awkward for him to suggest his own candidacy or to even discuss it with political rivals. "Walter Washington wans't going to end in an application. Somebody was going to have to call Walter Washington on the phone and say, 'Walter, the country needs you,'" the participant said.

"We were seriously presenting him for consideration. We believed that at the point when they began seriously considering him, they would contact him, he would send in a resume and the whole character of the thing would change," the source said.

The mayor did find out about the effort, however, and according to knowledgeable sources, discussed it on at least two occasions.

One was a social affiar at which the mayor mentioned the effort to R. Robert Linowes, a prominent Washington area lawyer who is Linowtiz's brother, one source said. The mayor told Linowes he was not interested, the source said: "He said he was the MAYOR. Just like that."

According to another source, the mayor also brought up the matter during a telephone conversation on an unrelated matter he had with party chairman Washington (who is not relation to the mayor). In a tone that seemed sarcastic, the source said, the mayor told Robert Washington. "I appreciated what you did for me."

Fauntroy, who less than a year earlier had accused the mayor of making a record of "waste and inefficiency," during the mayor's nine years in office, wrote a letter of recommendation to the advisory board. Other letters were also received, including one, a source said, from Humphrey, who had also served with Vance in the Johnson administration and whose advice was believed to be highly regarded in the Carter administration.

The deliberations of the advisory board are generally kept secret. Several sources on the board said, however, that they could not recall the mayor's name coming up in discussion of which names would go on the 30 lists of five persons each which the panel recommended be considered by the President.

The board made its recommendations by the end of March and has not met since because there is no other large group of pending diplomatic appointments, a State Department official said.

Fauntroy discussed the mayor's possible appointment with Vance for the first time at the June 18 Kennedys-King Dinner, a fund raiser sponsored by the D.C. Democratic Party. Vance was the keynote speaker at the dinner. At that time, Fauntroy said, he was told by Vance that the selection of the mayor was still being considered.

Although there is no fuiture meeting of the board scheduled, one board member, who asked not to be named, said he was approached about a month ago by someone at a party and urged to propose the mayor's appointment.

"All I know was that someone suggested to me that it would be a good idea," the board member said. "I tucked it in the back of my mind and at the next meeting I was going to suggest it. But there hasn't been another meeting so far."

A State Department spokesman confirmed yesterday that the mayor's name was still under consideration. What that meant, the spokesman explained, was that the mayor's name is still on a list of several hundred persons, "no less, no more."