The White House, resisting a budget-cutting proposal by a key congressional committee reaffirmed its support yesterday for a federal payment of $301 million to the District of Columbia for fiscal 1981.

President Carter submitted his proposals for trimming next year's federal budget and let stand the increase he had proposed in January.

The House Budget Committee, adopting new federal budget-cutting goals, recently voted to hold the federal payment to this year's level of $238.2 million -- an action that if approved by Congress could help throw the city's budget out of balance by as much as $100 million.

The District already has adopted austerity measures designed to prevent a deficit this year of up to $172 million. The Budget Committee proposal could extend the city's financial crisis into next year.

But Rep. Julian C. Dixon (D-Calif.), a native Washingtonian who took over last week as chairman of the House Appropriations District subcommittee, said he is prepared to ask the House to exempt the District's federal payment from the Budget Committee belt-tightening effort. A debate is expected to begin after Congress' Easter recess.

"I think that cut is not equitable and I will make that case," Dixon said.

Dixon said he would be joined by Rep. Louis Stokes (D-Ohio), a member of both the Appropriations and Budget committees, and Rep. Ronald V. Dellums (D-Calif.), chairman of the House District of Columbia Committee. A spokesman said Del. Walter E. Fauntroy (D-D.C.) also would participate.

While the budget document Carter sent to Congress yesterday does not specifically mention the District, a spokeswoman for the White House Office of Management and Budget said, "We support the federal payment [of $301 million] that was in the January budget. There is no change."

If the federal payment is cut by Congress, Dixon said he would have to "comb through" the D.C. budget -- on which he began hearings last week -- in search of places to slash. The federal payment is designed to compensate the city for taxes it cannot collect on federal and foreign embassy property and for unusual expenses caused by the city's role as the nation's capital.