Sen. Charles McC. Mathias Jr. (R-Md.), a longtime foe of proposals for a District of Columbia commuter tax on his constituents, suggested yesterday that regional officials look for a way to help pay some of the District's costs.

"I don't see how a giant metropolitan area like the national capital area can flourish without a great deal of fiscal cooperation," Mathias declared as the Senate D. C. Appropriations subcommittee began hearings on the city's budget for the 1980 fiscal year.

Although he said he still opposes a District tax on the incomes earned in the city by suburban residents, Mathias said he can see a case for the region helping shoulder the city's burdens.

He said regional contributions to the Metro transit system could provide a precedent and model.

Mathias made his comments to Mayor Marion Barry and Arrington Dixon, the City Council chairman, who were receptive, although Barry said he still thinks a commuter tax is a fair approach.

Dixon said he will take steps, as chairman of the Metropolitan Washington Council of Governments, to assemble a meeting of city and suburban officials to discuss the proposal. Mathias said he would attend "as a lightning rod to draw down the wrath from both sides."

The city's 1975 Home Rule Charter prohibits the city from levying a tax on the incomes of suburbanites, a provision city officials have tried repeatedly-and vainly-to get repealed.

Yesterday's hearing was an overview of a city budget that would provide $1.4 billion for municipal operations in the fiscal year starting next Oct. 1.

The budget is out of balance by $17 million, since current law permits the U. S. government to make an annual federal payment of up too $300 million to the city. With support from President Carter, city officials want that increased to $317 million.

The money is intended t compensate the District for its inability to collect taxes on federal property and activities in the city.

Across Capitol Hill yesterday, a House District subcommittee headed by Del. Walter E. Fauntroy (D-D.C.) voted 3 to 2 to approve legislation authorizing a $317 million payment.

Even if the legislation makes it through Congress and is signed into law by the president, the actual payment must be approved through separate congressional action.

A spokesman for Sen. Patrick J. Leahy (D-Vt.), who presided over yesterday's budget hearing, told a reporter there was "no way" Leahy would endorse any amount above $300 million. Last year, Leahy persuaded Congress to grant only $235 million.

In yesterday's House subcommittee vote, Fauntroy cast proxies granted him by absent Reps. Herbert E. Harris II (D-Va.) and Charles C. Diggs Jr. (D-Mich.).Reps. Millicent Fenwick (R-N.J.) and Bob Daniel R-Va.) cast opposing votes.

Fenwick accused the city administration of "not recognizing the Proposition 13 phenomenon," a reference to last year's California budget-cutting measure. Mathias, speaking at the Senate hearing, also said Proposition 13 has put the Senate in a budget-cutting mood and the District is not immune.

Mathias asked Barry whether the city was making any contingency plans to refund as much as $45 million the city has collected since 1975 in taxes on the earnings of professionals.

The tax was invalidated by a three-judge panel of the U. S. Court of Appeals. Barry said the city expects to ask for a rehearing before the full nine-judge court. "Obviously," he said, if the panel's ruling is made final "we will have to replace that tax with another tax." In the meantime, he told Mathias, no plans have been considered for a refund.