District Mayor Marion Barry plans to appoint seven members Monday to a new city commission created to make recommendations on the controversial issue of where to locate a new prison in the District, a city official said yesterday.

Barry had promised a Senate subcommittee that he would make the appointments a month ago and would give the commission a six-month deadline from then to come back with final recommendations on what kind of facility it should be and where in the city it should be built.

Barry signed legislation yesterday establishing the 15-member commission. Seven members are to be appointed by the mayor and eight are to be appointed by the City Council.

Hal Williams, an official in the office of the city administrator, said the mayor will announce his appointments Monday.

Barry had opposed building a new prison for the District to help relieve jail crowding, saying he preferred alternatives to incarceration.

Sen. Arlen Specter (R-Pa.), chairman of the Senate Appropriations subcommittee on the District, had pushed Barry repeatedly to build more prison space to deal with an expected rise in the city's prison population. At a subcommittee hearing this year, the mayor reversed his position and supported construction of a new facility on federal land within the city limits, using federal funding.

Specter has been pressing Barry to speed up the timetable for determining the location of a new facility, asking him to make a preliminary report by early August so the subcommittee can consider federal funding for the project when it approves the District's budget for fiscal 1986, which begins in October.

Also yesterday, Barry signed the fiscal 1985 supplemental budget bill that calls for spending $45 million more than the original $2.1 billion budget approved last year by the City Council.

The supplemental budget, which draws on a $41.7 million increase in city revenues that was not factored into the original budget, spreads appropriations widely across the gamut of general fund budget items, including increases in payments for personnel costs, emergency repairs for public housing, the summer jobs program for youths, expanded regulatory enforcement and lawsuits brought against the District.

The supplemental budget was approved by the council June 25. At that time, Council Chairman David A. Clarke reported that the city had made $11.3 million in overpayments to the D.C. Retirement Board fund. The council decided to apply $3.5 million of that money to help retire the general fund deficit and $2.3 million to fund pay raises for police officers, provided that an arbitration panel's ruling on the pay raises withstands an appeal by the mayor.