President Carter and Prime Minister Abel Muzorewa of Zimbabwe-Rhodesia spent much of their heralded meeting this week communing in individual and joint prayer while Secretary of State Cyrus R. Vance waited outside the meeting room.

In response to questions from The Washington Post, the State Department confessed yesterday it was "wrong" when it repeatedly asserted this week that Vance had been a participant in the 20-to 25-minute encounter at Holly Lodge between the president and Muzorewa, a U.S. educated Methodist bishop.

State Department officials refused to discuss what went on in the Carter-Muzorewa session.

The earlier statements from White House and State Department spokesman putting Vance in the meeting raised questions of credibility in the sharp conflict over U.S. policy toward Zimbabwe-Rhodesia.

Sen. Jesse A. Helms (R-N.C.), who is leading the drive to lift economic sanctions against Muzorewa'w government, is the bishop's host on his three-day visit to wash ington, Helms said before the Camp David meeting that he had asked Carter to exclude Vance and ot her foreign policy aides from the meeting so the two men "could get to know each other, free of the presence of others who might well create an implicit adversary atmosphere."

In belatedly acknowledging yesterday that the president had decided to stage the meeting just that way, State Department spokesman Hodding Carter told reporters that the decision did not in any way suggest a lessening of Vance's authority on the Rhodesia question or on foreign policy in general.

"The policy on Zimbabwe-Rhodesia is unchanged. To suggest that this building was cut out of the meeting is totally wrong," Hodding Carter said, adding that the president had met with about 40 "head state or head of government" without aides present.

But, the United States has not recognized Muzorewa's administration as being in power in the breakaway British colony. Other State Department and White House officials said their impression was that the president rarely kept foreign policy aides out of his meetings with foreign leaders.

Disclosure that the State Department was not in the Carter-Muzorewa discussions could have particular impact in black Africa. There, Vance, his aides and Ambassador to the United Nations Andrew Young have been seen as advocates of the search for a settlement that would include all parties including the Patriotic Front forces of Joshua Nkomo and Robert Mugabe.

Vance aides insisted yesterday that the three-day failure to acknowledge his absence from the meeting had resulted only from a series of misunderstandings and not from any attempt to mislead the public.

Speaking at his daily noon briefing, Hodding Carter said that the president and Vance had agreed before the meeting that a private one-on-one encounter would be best. A State Department official said during the briefing that the president thought more could be accomplished without the presence of other Rhodesian officials in the room, and Vance's absence apparently was seen as the key to this.

The controversy began almost as soon as Muzorewa returned by helicopted from Camp David and remarked in passing to Helms and a staff aide that he and Carter had met alone while Vance and two Zimbabwe-Rhodesian officials, Foreign Minister David Mukome and Cabinet Secretary George Smith, had sat outside the room in Holly Lodge.

Hodding Carter spoke to Vance late Wednesday afternoon and, unaware of the Muzorewa report, said afterward that the secretary had taken part in the meeting with the two other men. Another State Department official who spoke to Vance about the meeting a little later also left under the impression that the secretary had been in the session.

Pressed on the details at Thursday's noon briefing, Hodding Carter said flatly that "Vance met with them during a consideration portion of the meeting" on substantive matters. "He was with the president and Muzorewa for a considerable portion of the time."

But a detailed account of the circumstances of the meeting given to The Washington Post late Thursday night by Cabinet Secretary George Smith repeated Muzorewa's description and prompted a new query to Hodding Carter early yesterday. Carter at first labeled the account "a lie," then called back after talking with Vance to say that his earlier comment was wrong.

Vance accompanied Muzorewa to Camp David and went into the room where the meeting was to be held for a private conference with the president just before the one-on-one meeting. Vance came back out to introduce Carter and Muzorewa, the State Department spokesman said.

Asked what he had based his earlier statements on, Hodding Carter said they had come from "a secondary source" and not from Vance. He said he had not discussed "that aspect" - the question of whether Vance had been present at the meeting - with the secretary. The other State Department aide who talked to Vance also said that the question of Vance's presence had not been raised "and I just assumed he had been there."

After discussing the Rhodesian account with The Post and confirming its essential accuracy on the circumstances of the meeting, Hodding Carter went to his regular noon briefing and offered an apologetic acknowledgement of error. He did not suggest to reporters what had led to the acknowledgement. CAPTION: Picture, SECRETARY OF STATE VANCE . . . waited out 20-minute meeting