The White House has acted to stop its inflation fighters from blocking an agreement to resolve the nation's most expensive and longest-fought air cleanup controversy.

On March 9, Associate Attorney General Michael J. Egan authorized a letter to U.S. District Court in Nashville advising that a $1.2 billion air cleanup agreement between the Tennessee Vally Authority and the Environmental Protection Agency "is in the public interest and consistent with the president's policies." He cited Stuart Eizenstat, the president's domestic policy adviser, as authorizing the position.

While noting that there has been "some confusion" in the understanding of the administration's position, the letter says, "The executive branch is firmly of one mind in its support of the TVA agreement."

Barry Bosworth, director of the White House Council on Age and Price Stability, last fall wrote TVA protesting that the agreement, which relies on TVA use of new Appalachian coal supplies and air scrubbers, could have been accomplished more cheaply with western coal.

On Jan. 10, Bowsworth wrote to a TVA-area aluminum company saying that the agreement imposed "an unnecessary burden on the residential and industrial users of electric power in the Tennessee Valley."

That letter, made public by Consolidated Aluminum Co., set off a valleywide attack from businessmen, TVA power distributors and other who interpreted Bosworth's letter as being a White House position.

Appraised of the March 9 Egan letter through a spokesman today, Bosworth had no comment. Bosworth press aide Joe Carter, after checking with his boss, said the Egan letter should not be interpreted as a White House repudiation of Bosworth's Jan. 10 position.

"We're just a little part of government here looking at just inflation," Carter said. "We offer our little piece of evidence and assume other people offer theirs. Inflation is just a tiny sliver in everything."

TVA Chairman S. David Freeman said today he had no comment on the Egan letter except to say, "I'm perfectly willing to quit winners on the matter," Earlier, Freeman, who had ignored the Bosworth letter, said the inflation fighter "doesn't have the foggiest idea of what he is talking about on this subject."

The TVA cleanup, which will remove 14 percent of the utility-emitted sulfur dioxide gases from the nation's air, was negotiated last year by presidential appointee Freeman. It was not official until nearly a year later, however, because Nixon administration appointees on the TVA board refused to sign it.

TVA the nation's largest coal buyer, has repeatedly said it does not believe it is in the national interest to buy western coal because that would disrupt the eastern coal economy and waste locomotive diesel fuel. Bids submitted to TVA from the West on several occasions showed western low-sulfur coal to be no cheaper than eastern supplies, TVA claims.

Earlier this week, before the Carter administ ration position was known, Freeman attacked critics of the air cleanup agreement as "mistaken" in believing it was inflationary. He said the additional cost would be more than offset by improvements in public health and increased reliability for TVA steam plant boilers that frequently choke on the low-quality coal dumped into them.

The out-of court agreement must be approved by U.S. District Court Judge Tom Wiseman in Nashville, who has asked TVA for an inflation impact statement on the settlement. Egan's letter was directed at clearing up any confusion the court might have had about the adinistration's position. Bosworth's Jan. 10 letter was sent by several critics of the agreement to the judge. The new Justice Department letter, outlining the administration's position is expected to be in the court record next week.

The agreement is expected to raise TVA's residential rates approximately 10 percent in the next four years.