Bush Delay on Naming His Chief of Staff Told : He Reportedly Is Seeking Suitable Job for Fuller; Jews in U.S. Hit Sununu Over a U.N. Resolution

President-elect George Bush delayed announcing his choice for the crucial post of White House chief of staff--almost certain to be New Hampshire Gov. John H. Sununu--while seeking a suitable job Wednesday for his current staff chief, Craig Fuller, sources close to the vice president said.

But even before an appointment for Sununu could be announced, the governor drew fire from Jewish groups over his refusal two years ago to sign a statement condemning a United Nations resolution that equates Zionism with racism. He was the only governor of 50 who balked at supporting the statement.

Bush was typically closemouthed about the status of his efforts to assemble a senior White House staff and fill the 12 remaining positions in his Cabinet--the most immediate tasks in his transition to the presidency.

‘Stay Tuned’

At the start of a White House meeting with visiting Soviet human rights activist Andrei D. Sakharov, he told reporters: “No final decisions . . . stay tuned.”

At a press conference in Concord, N. H., Sununu refused either to confirm or deny his impending appointment. “It isn’t over until the tall, thin guy sings,” he said, in a reference to the lanky President-elect.

Sources involved in the transition effort portrayed Bush as impatient to fill the job. But one said that he wants to be able to make a simultaneous announcement of a post for the 37-year-old Fuller, the other top candidate for the post, to avoid bad feelings.

“Bush is kind of anxious to get Sununu in place so Sununu can start filling up the other key jobs”--those of national security adviser, congressional liaison and press secretary, a Bush adviser said.

Of Fuller, “I guess they make him secretary of transportation or he goes home or he just becomes another one of the people who’ve been banished, the former Bushies,” said a senior Republican close to the transition team. “Of course, the irony is, Fuller’s done this to others.”

For his part, Fuller, who has headed the vice president’s staff for four years, brushed off suggestions of a feud with Sununu. “I have had only, only friendly and good working relationships with John Sununu. I count him as a friend. I count him as somebody who could offer an awful lot to the country, should he come to Washington,” Fuller said at a news briefing.

The criticism of Sununu came from the Anti-Defamation League of B’nai B’rith and Rabbi Marvin Hier, director of the Simon Wiesenthal Center in Los Angeles.

Abraham H. Foxman, the league’s national director, said in a statement issued in New York that a possible choice of Sununu “raises some concerns.”

Hier said that “there’s a lot of concern in the Jewish community” about Sununu’s refusal to sign the statement. “The selection will not meet with wide approval in the Jewish community.”

Sununu’s aides have said that the governor, who is partly of Lebanese descent, balked at signing the statement circulated among the nation’s governors, not out of sympathy for the Arab cause, but because he believed that state officials should not involve themselves in foreign policy.

Several colleagues in New Hampshire said that Sununu would bring strong organizational skills to the chief of staff’s job.

‘Hands-On’ Style

Sununu, whose third two-year gubernatorial term is about to expire, would be “a very hands-on chief of staff, involved in everything, big or little, that goes through that office,” said Jay Smith, a political consultant who worked on Sununu’s state campaigns.

“His greatest strength is he’s brilliant. His biggest weakness might be a lack of tolerance for people or processes that don’t go his way, according to his timetable,” Smith said. “He has to work on his patience.”

In the roster of other highly visible positions in the new Administration, one source close to Bush speculated that Zbigniew Brzezinski, President Jimmy Carter’s assistant for national security affairs and a Bush supporter in the 1988 campaign, may be in line for the post of U.N. ambassador.

This source said that Bush is likely to name retired Air Force Lt. Gen. Brent Scowcroft to serve as White House national security adviser, as he did in the Gerald R. Ford Administration. Scowcroft also has been mentioned as a possible candidate to head the Central Intelligence Agency if William H. Webster is asked to leave that post.

Other Candidates Listed

In other developments, a White House personnel consultant said that the following people are being considered for possible senior-level jobs:

--Former Tennessee Gov. Lamar Alexander, president of the University of Tennessee, as secretary of education, replacing recently appointed Lauro F. Cavazos.

--Robert Mosbacher, a long-time friend of Bush from Texas and campaign fund-raiser, as commerce secretary.

--Everett Alvarez, former deputy administrator of the Veterans Administration and the longest-held American prisoner of war in Vietnam, as secretary of the new Veterans’ Affairs Department. If Cavazos does not retain his education post, such an appointment would allow Bush to honor his pledge to appoint a Latino to the Cabinet.

--New Mexico Gov. Garrey E. Carruthers as Interior secretary.

Other sources said that Rep. Bill Gradison, a moderate Ohio Republican, and Rep. Lynn Martin (R-Ill.) are in the running for secretary of health and human services, while members of the party’s right wing push for a more conservative leader for the department.

Bush has named former Treasury Secretary James A. Baker III, his longtime confidant, as his choice for secretary of state, and another friend, Nicholas F. Brady, who already has replaced Baker at the Treasury, to retain that post.

Attention remains focused on former Sen. John Tower (R-Tex.) and Paul H. O’Neill, chairman of the Aluminum Corp. of America, as the leading candidates for secretary of defense.

Meanwhile, conservatives who earlier seemed opposed to Dick Thornburgh’s continued tenure as attorney general appeared to be backing down in the face of the possibility that he would be replaced by someone they would like even less.