An increase in the federal payment to the District of Columbia, to a record $317 million, and a cutback of federal-impact aid funds to the region's suburban school systems were proposed yesterday by President Carter.

In his 1979 budget, the president also asked Congress to provide $55 million for a major renovation of St. Elizabeths Hospital and $18 million to buy land for a new Government Printing Office, a project with a total price tage of $164 million.

Both the increase in the U.S. payment to the District of Columbia and the reduction of impact aid to the schools encountered immediate resistance in Congress. The proposed cut of impact aid is less severe than that proposed by previous administrations.It would trim $58 million from a program that is costing more than $800 million this year.

The two chairmen whose congressional panels on District of Columbia affairs must consider the federal payment increase - Sen. Thomas F. Eagleton (D-Mo.) and Rep. Charles C. Diggs Jr. (D-Mich) - both have doubts the legislation will be approved, aides said.

The federal payment is intended to reimburse the District of Columbia for the taxes it cannot collect on government-owned property, as well as for services the city provides. Current law limits the payment to $300 million. The payment this year, under a stopgap appropriation, is $276 million.

The increase to $317 million was endorsement last year by a White House task force on District of Columbia problems. Legislation that would authorize that outlay was received by the House District Committee yesterday from Mayor Walter E. Washington and will be introduced by Diggs as a basis for hearings.

An aide to Eagleton said the senator is opposed to any higher federal payment "until D.C. trims back its overly large payroll." An aide to Diggs said the congressman sympathizes with the city's request but "does not feel the increase is feasible" politically this year.

D.C. Budget Director Comer S. Coppie said "there is no question that we can justify the level (of $317 million) as proposed by the president."

Although the presidential budget contains various federal cash contributions to the city and a long list of government projects affecting the entire region, the D.C. budget itself will be sent to Congress separately in February.

The impact-aid program reimburses 4,300 school districts across the nation for part of the cost of educating the children of federal employes and military personnel. The District of Columbia and the Washington suburbs are among the biggest beneficiaries.

Every president since Eisenhower has sought to eliminate or sharply curtail the program, but it has survived.

Carter's proposed cutback would eliminate payments for children whose parents work on federal property outside the county in which the school district is located - for example, payments to Fairfax County for children whose parents work in the District of Columbia or Arlington.

Calling this "simply not fair," Rep. Herbert E. Harris (D-Va.), whose district includes part of Fairfax, said he would ask the House Budget Committee to keep the present program intact.

Harris' office said the Carter proposal would mean a loss of $3 million from the current payments of $15.5 million in northern Virginia and a loss of $1.7 million from payments of $8.8 million in suburban Maryland. The District of Columbia would not be severely affected.

The $55 million proposed for renovation of St. Elizabeths is intended to put the mental hospital into shape for full accreditation and an eventual transfer from the Department of Health, Education and Welfare to the D.C. government.

The $18 million for GPO would buy a 33-acre site on Brentwood Road NE, near the Union Station yard. Legislation to authorize the GPO construction project is pending in Congress.

The presidential budget omits $6million requested by the National Fire Prevention and Control Administration for a national fire training academy at the old Marjorie Webster Junior College in northwest Washington. The project is being restudied under a directive of the Office of Management and Budget, and a report is due in the spring.

Following are some other items affecting the area that are included in the presidential budget:

$582,000 for repairs on the Chesapeake & Ohio Canal, including $196,000 in and near Georgetown.

$4.2 million for maintenance of the Capitol grounds, double what is being spent this year.

$10 million for construction projects at Howard University, including the conversion of the old Freedmen's Hospital into a classroom building.

$10.5 million in construction projects at National and Dulles airports, including improved runways and the enlargement of the Dulles baggage claim area.