Labor leaders and White House officials are not as divided over President Carter's program to slow wage and price increases as their public statements suggest, officials of the AFL-CIO and the Carter administration said privately yesterday.

Both sides are quietly trying to repair any damage that was done after a tense White House meeting with the AFL-CIO Executive Council last Wednesday when Carter sought, and failed to get, a commitment from AFL-CIO President George Meany that the federation's 105 member unions would seek smaller wage increases in upcoming bargaining.

"The reponse from the AFL-CIO was not all that bad," one senior White House official said yesterday.

"It came reasonably close to what you could expect, but only came after a very tough meeting," the official said.

AFL-CIO spokesman Allen Zack agreed. He said that the president's top inflation adviser, Robert S. Strauss, asked Meany for four things, all of which Meany delivered in a public statement after the meeting.

Meany applauded Carter for his desire to reduce inflation, recognized that inflation hurts all Americans, supported the president's voluntary approach, and said progress in holding down price increases would automatically bring down wage increases.

It was also learned that Meany, who will appear tomorrow on "Issues and Answers" (ABC, WJLA), is prepared to say that efforts will be made to hold down wage demands if the president devises a satisfactory mechanism to slow price increases.

Neither the administration nor the AFL-CIO wants so spark a serious fight over the president's voluntary program to hold down the rate of inflation. The administration needs labor support not only on inflation but also on such issues as civil service reform. Labor needs the administration's lobbying on labor law revision, which is scheduled to go to the Senate floor next week.

One source close to administration officials at the Wednesday meeting said the public spat could bring both sides closer, in part because it has helped to clear the air.

Zack said labor was "quite pleased" by a statement from Barry Bosworth, director of the Council on Wage and Price Stability, that not all unions should be expected to seek smaller wage increases.

Bosworth told The Washington Post Thursday that instead of expecting each union to reduce its wage demands, that unions with small incrases over the last three years should be asked to hold the line while unions that received big wage increases might be asked to reduce their wage demands even more.

The president is seeking an average reduction of half a percentage point in wages and prices.

Zack said the ideas Bosworth broached were those "we thought came out of the meeting too . . . If Bosworth had that feeling and if Strauss got what he asked for, then there shouldn't be any disagreement."

Zack noted that Meany volunteered in his statement that inflation was the nation's number one problem and that the 39 percent coal settlement reached in late March should not be a model for others.

But a senior White House official, while trying to sound conciliatory, noted that there has not been a real signal from labor leaders that they want to cooperate on a case-by-case basis.

Labor leaders believe that Meany tried to be conciliatory in the meeting and afterward, and that while neither Carter nor Meany has been successful in dealing with one another, there has been no increase in hostility between the two, at least on Meany's part.

But they continue to believe that the administration doesn't fully understand the political problems labor leaders face in trying to persuade their members to reduce wage demands.