The chairman of the House D.C. Appropriations subcommittee warned Mayor Marion Barry yesterday that the city's $63 million supplemental budget request will be held up until he gets a satisfactory explanation of the city's newly disclosed fiscal problems and how Barry plans to solve them.

Rep. Julian C. Dixon (D-Calif.), chairman of the subcommittee, said he and other members of his committee had been told by Barry at a May hearing on the supplemental budget that there was no chance of a reoccurence of the kind of financial problems that recently have plagued the city.

But recent reports from the D.C. Department of Finance and Revenue have disclosed that city revenues are coming in at a level $12.9 million below that forecast, raising the possibility of a deficit of at least $5 million up to $6 million when the fiscal year ends Sept. 30.

"There will be no further action until we receive some response from them," Dixon said in an interview yesterday. "I've asked for it as soon as possible, immediately if not sooner."

On Tuesday, Barry suggested that $10 million set aside for a long-term debt service could be used to cushion a revenue shortfall. But Dixon said yesterday that would violate Congress's intent when it approved the $1.6 billion operating budget for 1982.

A spokesman for Sen. Alfonse M. D'Amato (R-N.Y.), Dixon's Senate counterpart, said D'Amato also has asked his staff to request information from Barry on the possible deficit developing in the budget. D'Amato's aide said the senator has suspended any judgment on whether to approve the city's supplemental budget request until the House committee acts on it in late July.

City administrator Elijah B. Rogers said yesterday that his staff is already preparing a status report that he hopes to have ready for Dixon an D'Amato by Friday.

Rogers said the report will also include new revenue projections for August and September, the last two months of the fiscal year, and unveil his plan for reductions in spending to insure that the budget remains in balance. The $12.9 cumulative shortfall stems primarily from lower than anticipated revenues during the months of May and June.

"I've talked to the chairman twice today," said Rogers, "and he indicated he wanted a status report. It's a reasonable request. He's been a supporter of the District and chairman of our subcommittee. I gave him some reassurances. We had a dialogue and I'm 98, 99 percent sure that the House and Senate will approve our supplemental request."

Earlier in the day, Dixon said he had been given no hint that the city was encountering budget problems, but added that a preliminary review of the city's May and June shortfalls indicated that part of the problem was the nationwide downturn in the economy. Dixon said he still would have wanted some warning of the approach of a possible deficit.

On Thursday, the ranking minority member of the committee, Lawrence Coughlin (R-Pa.), complained that the committee had been "flim-flammed" by Barry's claims to have the budget under control and said he would press for a delay in action on the supplemental budget until the committee received an explanation from Barry.

Congressional sources said yesterday that several congressmen fear that a full hearing of the city's fiscal troubles, which is likely to draw intense public attention, could be seen as an attempt to damage Barry's campaign for reelection. So Dixon decided instead, sources said, to ask for a written report.

"Today I have drafted a letter to deliver to the mayor that indicates we have some concern about information about the shortfall in revenues," Dixon said, "and have asked him for his best estimate of the shortfall and to document his best estimate of revenues through the balance of fiscal year ending Sept. 30."

Dixon said he also asked Barry to inform the subcommittee of what cuts in city programs would be made to compensate for the shortfall in the remaining two and a half months in the fiscal year.

City budget officials have said that the District could encounter even more financial woes if the supplement is not approved, since many of the funds already are committed to programs that would have to be drastically reduced if the additional monies were not available.