Mayor-Elect Sharon Pratt Dixon urged outgoing Mayor Marion Barry yesterday to submit a plan to the D.C. Council for closing a possible $200 million budget deficit "by whatever means possible," but declined to say whether she thought a tax increase was necessary.

"I don't presume to second-guess, nor am I going to Monday morning quarterback whatever decisions they might reach," Dixon said at a joint news conference with Barry. "It is the responsibility of the outgoing administration . . . to balance the budget."

Her position drew an angry response from John A. Wilson, the council's chairman-elect, who said he and his colleagues are not willing to sign off on a tax and budget-cutting package for fiscal 1991 without Dixon's concurrence.

"If the council is going to deal with any tax increase or budget cuts, they want to know what the mayor-elect's position is," Wilson said. "What she's saying is, 'You all raise taxes, you all balance the budget, and I'll stand here and say nothing.' It is not that simple."

Dixon campaigned on a platform of no new taxes and deep cuts in the District government bureaucracy, although she has begun to hedge on whether some additional tax revenue will be necessary. Wilson, who intends to play a leading role in the city's budget debate, is pressing Dixon to indicate before taking office whether she would go along with tax increases as part of a package to balance the $3.5 billion budget.

Wilson, currently chairman of the Finance and Revenue Committee, contends that the financial crisis can only be solved by a full package of budget cuts and tax increases and a substantial boost in the federal payment to the District. He has also been adamant that the council not proceed with tax increases unless Dixon first agrees.

"My position is that the boat does not leave the dock until everybody is on it," Wilson said after an hour-long meeting with Barry and Dixon yesterday afternoon to discuss the mounting fiscal crisis.

Although the new administration does not take office for seven weeks, jockeying over the budget has already begun in earnest because of the timetable of the District's budget process and the depth of the financial problems. Within a month of taking office, Dixon must propose a balanced budget for fiscal 1992, which begins Oct. 1, 1991.

The city, meanwhile, must also balance the budget for the current fiscal year, for which officials are already projecting a $100 million to $200 million deficit unless steps are taken to reduce spending or raise revenue.

Barry was prepared to submit a revised budget to the council, which he said would have included more than $50 million in additional revenue and more than $40 million in spending cuts. However, he changed his mind and announced last week that he would not submit the supplemental proposal, thus putting pressure on Dixon to come up with her own budget-balancing proposal for the current fiscal year.

The council placed more pressure on Dixon Tuesday by voting to reject Barry's proposed 2 percent pay increase for city workers, a measure that would have cost the city about $31 million. Now Dixon must tackle the politically difficult task of renegotiating a wage agreement with the municipal unions at the same time she is likely to ask labor to accept reductions in city manpower.

During the news conference, where Barry presented Dixon with six large transition briefing books, the mayor-elect declined to take a position on the pay increase issue. She said it was up to Barry to leave her a balanced budget when she assumes office Jan. 2. Dixon also said it is her hope that Barry will submit a revised spending plan before he leaves office.

"I am not in favor of any type of tax increase," she said, though she suggested that she would not object if Barry and the council agreed to one on their own.

"I'm not going to Monday night quarterback. I'm not going to say after the mayor makes his decision how I would do it," Dixon said. "It's his decision . . . . I'm simply asking him to leave a balanced budget."

After his meeting with Dixon, Barry issued a statement reiterating his decision not to submit a supplemental budget.

"Since the mayor-elect has taken a stand against any increased taxes and the majority of the council members do not support any tax increases, it is futile for me to submit a supplemental budget," Barry said. "Without the support of the mayor-elect, the measure just wastes everyone's time."

Barry said it is "not unusual" for a supplemental budget to be submitted in the new year, and he added that Dixon "will have ample opportunity to use the supplemental budget process to offer a balanced budget to the council once her term begins."