Presidential economist Murray Weidenbaum appeared yesterday to back off somewhat from the administration's commitment to keep next year's budget deficit to the $42.5 billion forecast in July, although he later said that it was the administration's "best estimate" and that officials are "doing our best to achieve it."

Weidenbaum told reporters at a breakfast meeting that he could "only regard" the $42.5 billion "as an estimate," rather than a commitment. Just two weeks ago, the president reaffirmed the $42.5 billion deficit target in answer to reporters' questions. Officials yesterday denied that there was any disagreement within the White House over the status of the $42.5 billion figure, which many outside experts believe cannot be reached.

Fears that next year's deficit could reach $60 billion have been a major contributor to the marked weakness in financial markets this summer. An unpublished forecast from the Congressional Budget Office shows the budget gap at almost $60 billion next year, and one source described even this as optimistic.

However, White House spokesman Larry Speakes repeated yesterday that the White House would stay with its prediction for next year's deficit. Weidenbaum explained that there was "a season" for making forecasts, and officials would not rework their last estimates until the next forecasting round for publication in January.

He drew a distinction between the "estimate" for next year's deficit and the administration's aim of balancing the budget by 1984. He said of the balanced budget, "We are very much engaged in an effort to achieve that goal."

Since the July forecasts were made, interest rates have remained stubbornly high, whereas the administration expected them to fall sharply. High rates add to the cost of the government debt, and so push up spending directly.

This is one reason why outsiders put next year's likely deficit higher than the administration's number. The August slump in bond markets has put considerable pressure on the administration to find more spending cuts to hold down next year's deficit.

Officials have warned that Congress must make further cuts in the 1982 budget just to keep to its spending ceilings announced earlier this year.

Most outside experts, including supporters of the Republican adminstration, do not believe that the administration can balance the budget by 1982 because they think it will be impossible for Reagan to win all the further spending cuts needed.