Jack M. Eckerd announced his intention to quit as head of the General Services Administration late yesterday, accusing the White House of injecting politics into top GSA appointments despite President Carter's promise to remove the agency from politics.

Eckerd's announcement came after he lost the right to name his own top deputy, in the first clear struggle over political patronage to surface publicly within the Carter administration.

"One of our major accomplishments during the past 15 months has been the removal of politics from this agency," he said in a late afternoon statement. "This order from the White House indicates I would not be able to maintain this record."

White House press secretary Jody powell announced yesterday that the agency's No. 2 job would go to Carter's choice, Robert T. Griffin, a longtime friend of House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.).

In a telephone interview, Eckerd, a Florida Republican who had been asked by Carter to stay on, said Griffin was chosen "because Tip O'Neill wanted him in, that's my understanding."

O'Neill has been reported angered by earlier appointments of people from Massachusetts without his prior knowledge. Last week Carter named O'Neill's son to a commission designed to remove politics from ambassadorial appointments.

Eckerd said he discussed the job with top Carter aide Hamilton Jordan last week, and "I . . . had a firm understanding I thought with Mr. Jordan that Gen. [Wallace H.] Robinson was going to be my deputy administrator."

Robinson, a former Marine Corps general who headed the Defense Supply Agency, is the GSA's acting deputy director.

"I told him [Jordan] that I had the right man for my deputy spot, Gen. Robinson, and I expected to keep him . . . He agreed to it," Eckerd said.

Powell said yesterday that Carter believes the dispute resulted from "an honest misunderstanding" after Eckerd talked with Carter at the White House Feb. 4.

Eckerd left that meeting thinking he had Presidential approval to choose his own deputy, Powell said, but the choice had always been Carter's to make.

Eckerd said during the interview he does not remember the subject being discussed in the Feb. 4 meeting.

His first inkling of trouble came Monday, he said, when Carter called to say that Griffin "was a commitment made weeks ago by his staff, and that he felt he had to live up to that commitment."

"I replied that I couldn't live with that," Eckerd said. "His reply was that he wanted to live up to his commitment to me, and also felt he had to live up to any commitment made by his staff, because they were speaking on his behalf."

Carter told him to think the situation over, Eckerd said.

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The President called Wednesday afternoon to ask if he'd made a decision, Eckerd said, and during a meeting later that day, "I told him I was afraid there was no way he could live up to both of those commitments. He said he was sorry about that. I asked him when he would like my resignation. He said at my convenience."

Late yesterday afternoon, Eckerd said, Carter sent over a hand-delivered letter asking for his resignation.

In his statement, Eckerd said the White House order to appoint Griffin "put me in an untenable position."

When Powell announced Eckerd's intention to leave, he was asked if Jordan had worked out a deal with O'Neill to put Griffin in, and just hadn't informed the President.

"No," Powell replied -

When the White House announced this week that Carter had asked Eckerd to say on in his job, Powell said the President "feels it important that the GSA job not be political."

The President "still intends" to make GSA a non-political agency, Powell said. Eckerd, appointed by President Ford, has won praise for reducing political influence in what had been a patronage-ridden agency.