The Washington Post yesterday apologized to former president Carter and his wife for an item that appeared in the Ear column Oct. 5 about reports that Blair House had been bugged during President-elect Reagan's stay there in January.

The apology came in the form of a letter from Post Publisher Donald E. Graham to the Carters.

"I wish to retract the item that appeared in The Washington Post," the letter began. "When we published the item we had a source whom we believed to be credible and reliable, and he identified his sources as two members of your family," the letter read.

"We now believe the story he told us to have been wrong and that there was no 'bugging' of Blair House during your administration. Nor do we now believe that members of your family said Blair House was 'bugged.' " The Post has not identified its source.

The letter came two weeks after the Carters had demanded an apology and threatened to sue The Post for libel.

Washington Post Executive Editor Benjamin C. Bradlee yesterday declined comment on whether the letter was written as part of an agreement negotiated with the Carters to avoid a lawsuit.

Carter's local attorney, Terrence Adamson, also declined comment on any possible agreement between the parties. "The president has not yet had a chance to read the letter and neither have I," he said.

"Apparently it says something different from what The Post has been saying before, something kind in nature. We've said from the start that we would take The Post's response into account in deciding whether to sue."

Former presidential press secretary Jody Powell said last night that Carter will have a response to the letter today.

When Carter first sent his letter, the paper had no immediate response. Six days later, it published an editorial that said, "It is one thing, however, to read that item to say that such a tale is circulating . . . and quite another to conclude from this that the place was in fact bugged . . . Based on everything we know of the Carter instinct and record on the subject, we find the rumor utterly impossible to believe."

The editorial itself created controversy. Powell noted the day it was published that the "Post is taking the position that there was nothing wrong with printing a rumor it believed to be false."

Yesterday, the paper printed 12 letters-to-the editor sharply critical of the editorial. Various media observers also have attacked the paper for its stance.

Graham's letter sought to clarify the editorial.

"The editorial, which spoke for the management of the paper, did not intend to suggest that the paper prints rumors which it knows to be false, because that is not the policy of The Washington Post," it said.

The flap began with an item in the Post gossip column that referred to a "hot new twist" on the tale that Nancy Reagan wanted the Carters to move out of the White House prior to the inauguration so she could get a headstart on redecorating.

The text of Publisher Donald Graham's letter to the Carters:

Dear Mr. President and Mrs. Carter:

I wish to retract the item that appeared in The Washington Post concerning reports that Blair House was "bugged" during President-elect Reagan's stay there. I also wish to apologize to both of you for its publication and regret any embarrassment that it caused you. As The Post noted in its editorial of Oct. 14, your record in matters pertaining to the right of privacy is worthy of the highest respect.

When we published the item we had a source whom we believed to be credible and reliable, and he identified his sources as two members of your family. To our knowledge he had also told his story to high members of the Reagan administration and to others. We now believe the story he told us to have been wrong and that there was no "bugging" of Blair House during your administration. Nor do we now believe that members of your family said Blair House was "bugged."

I would like to take the opportunity to clear up the misunderstanding that followed our editorial of Oct. 14.

The editorial, which spoke for the management of the paper, did not intend to suggest that the paper prints rumors which it knows to be false, because that is not the policy of The Washington Post. Our policy is to print news that is accurate from sources we believe to be reliable. We try to correct any published information we later find to be untrue, and that is what we are doing in this case.

Sincerely,

Donald E. Graham