Elected officials from Montgomery and Prince George's counties performed a rite of winter today, asking Maryland's sitting governor to increase state aid to their jurisdictions by millions of dollars.

In separate meetings with Gov. Harry Hughes this afternoon, four Montgomery officials appealed for school construction and transportation money, and the Prince George's state Senate delegation asked for an additional $2.5 million to finance a magnet schools program.

Hughes made no promise to increase his proposed $3.5 million appropriation for magnet schools, the centerpiece of county desegregation.

Nor did the governor promise Montgomery officials that their fast-growing county would receive a requested $10 million for new schools or $3 million for the local Ride-on bus program. Hughes' 1986-87 budget included no Ride-on subsidy but did contain $5.5 million for new schools in upper Montgomery.

County Executive Charles W. Gilchrist, County Council President William E. Hanna Jr. and the head of the local House and Senate delegations argued that because the affluent county generates millions of tax dollars for the state, it deserves a larger piece of the financial pie.

"We have a legitimate case and I think the governor was sympathetic to us," said state Sen. Sidney Kramer (D-Montgomery). "But we have no promises."

Wayne A. McDaniel, the governor's transportation adviser, who attended the meeting with Montgomery officials, said Hughes may provide Ride-on money in a budget amendment.