The House District Committee voted yesterday to make D.C. Del. Walter E. Fauntroy the new chairman of its subcommittee on fiscal affairs and health, a move that would give the city more influence on the congressional panel that oversees its legislative affairs.

The action still would have to be approved by the House Democratic Caucus, because it requires a waiver of a rule limiting members to one subcommittee chairmanship.

Two years ago, Fauntroy gave up chairmanship of a District subcommittee to head the House Banking subcommittee on domestic monetary policy, though he remained a member of the District Committee.

At the time, Fauntroy had to defend his switch, saying it would not lessen his ability to promote the interests of the city. He said then that he would use his new position on the banking panel to give the District's problems greater exposure.

If yesterday's action is approved by the caucus, Fauntroy would regain more direct authority over city issues without having to give up a forum for national issues.

Johnny Barnes, Fauntroy's committee staff aide, said the most important bills coming before the District panel this year will go through the fiscal affairs subcommittee. These will include authorization of the federal payment to the District, proposed changes in how that payment is determined and proposed revisions in congressional review of District legislation.

Staff aides to Fauntroy now say there is ample precedent for allowing District Committee members to have dual subcommittee chairmanships. House District Committee Chairman Ronald V. Dellums (D-Calif.), for example, recently was approved as chairman of a House Armed Services subcommittee without having to give up his other chairmanship.

However, Fauntroy said through a spokesman that he did not want to comment until the action is ratified by the caucus.