Virginia Gov. John N. Dalton's administration forecast yesterday that President Reagan's budget cuts will leave the state with a $93.5 million fiscal gap during the next nine months and cautioned that the shortfall may go higher.

Dalton, a strong Reagan supporter, asked the General Assembly for "limited" special authority to juggle funds within the current state budget to try to offset the federal cutbacks. His aides sought, nevertheless, to play down the effect of the congressionally approved reductions.

"The projected impact on Virginia does not appear to be catastrophic and does not appear to be unmanageable by any stretch of the imagination," said Charles J. Davis III, the governor's press secretary. Dalton "supports the president's program. He realizes that there will be belt-tightening necessary," Davis said.

State officials said the estimated $93.5 million deficiency for Virginia's current fiscal year probably could be absorbed without substantial damage to state programs. But senior state administrators expressed concern yesterday about the prospect of additional Reagan-backed federal cuts. Congress authorized major reductions, chiefly in social service programs, in July and may trim federal aid further this fall.

The new estimate of Virginia's financial gap -- the firmest yet provided by state budget analysts -- was presented to legislators at a special one-day General Assembly session in Richmond. The legislators scheduled committee consideration of Dalton's request for later this month and promised to act on it at an Oct. 5. session.

Dalton sought the budget-transfer powers because the federal cutbacks are to take effect Oct. 1 and the legislature will not start its biennial budgetary session until January. Federal aid normally accounts for nearly $1.6 billion of Virginia's $5.9 billion yearly budget.

Aides to the gubernatorial candidates, Republican J. Marshall Coleman and Democrat Charles S. Robb, rivals in November's elections, responded guardedly to the newly announced fiscal estimates. Although the Dalton administration is currently drawing up a proposed budget for the coming fiscal year, Dalton's successor in January will inherit the main task of coping with Reagan cuts.

"It's a bit premature to comment on how we're going to deal with it," said Coleman's press secretary, David Blee, expressing support for Dalton's approach. "We think we can make ends meet without a tax increase."

Robb's spokesman, George Stoddart, said the Robb camp was "not going to be specific" about where the state budget should be trimmed. But he noted that the new estimates were in line with previous forecasts and reiterated Robb's opposition to tax increases and his view that education programs should be regarded as a "sacred cow."

According to state officials, a key factor in Virginia's capacity to absorb federal cutbacks is an $81 million surplus run up by the state government during the state's last fiscal year, which ended June 30. Officials said this may be used, at least in part, to offset the anticipated shortfall of federal funds.

Ray Sorrell, acting director of the state Department of Planning and Budget, said the principal cuts in federal aid to Virginia would affect social service programs.

Among these, he said, would be a $9.8 million shortfall in Medicaid, which provides health care for the poor; an $11.2 million deficiency in welfare programs, such as food stamps and aid to families with dependent children, and a $32.5 million reduction in Comprehensive Employment and Training Act (CETA) programs. The Reagan-backed budget cuts eliminated CETA's public service jobs projects altogether.

The estimated deficiency is based on a comparison of the amount of federal money Virginia now expects to receive and the amount the state would spend on federally assisted programs if they continued as they are currently operating.