The House Appropriations Committee, in an action without known precedent, voted yesterday to finance District of Columbia government operations for the entire 1978 fiscal year without enacting a formal budget.

The committee's approval of a continuing resolution expiring next Sept. 30 followed a breakdown of negotiations by House and Senate conferees over the city's plan to build a $110 million downtown convention center.

Testerday's action came as a surprise. A resolution covering a shorter period, perhaps until Feb. 28, had been expected in order to buy time for a possible agreement on the center.

The measure may come to vote, in the full House today, with Senate action to follow. Sen. Patrick J. Leahy (D-Vt.) chairman of the Senate Appropriations subcommittee on the D.C. budget, said he would support Senate agreement with the House measure.

If it chooses to do so in the coming months, Congress still could enact a city budget, with or without funds for the convention center.

The House proposal would be a face-saving device for Rep. William H. Natcher (D-Ky.), veteran chairman of the House's D.C. budget subcommittee and a strong opponent of the convention center as proposed by city officials. He won an overhelming vote of support on the Senate floor, and has told Natcher he would not back down.

The resolution would keep the convention center project alive, which Natcher wants, while preventing a start of work on it. "Basically, it upholds the Senate's position," Leahy told a reporter.

Leahy said he had issued an open invitation to Natcher for the conference committee to meet an any time on the city budget, and to look for alternation proposals for the center project provided Natcher would agree to knock it out of the 1978 budget.

Natcher could not be reached for comment. After two inconclusive sessions of the conference committee, has refused to attend further meetings.

Mayor Walter E. Washington said he was "surprised and obviously distressed that we have to project a full year without a budgeT. I would hope for an early and favorable resolution."

Althought D.C. financial officials were unable to spell out its possible effects, the resolution would probably result in the city not having enough money to operate all of its programs at proposed levels for the full year.

The measure would permit the city to spend in fiscal 1978 the same amount spend in fiscal 1977, and at the same pace. Municipal spending in fiscal 1977 was $1.1 billion.

The city's need for 1978, reflected in the proposed budget caught up in the House-Senate deadlock is at least $100 million greater-due in part to wage increases for city workers.

Enactment of the continuing resolution also would wipe out Washington's capital outlay (construction) program for the entire fiscal year. Such projects as the new Mount Vernon Square campus of the University of the District of Columbia and a new municipal office building could not be undertaken.

Yesterday's events on Capitol Hill overshadowed a skirmish between Mayor Washington and the D.C. City Council over the proposed city budget for fiscal 1979, which begins next Oct. 1.

The council, by voice vote and without a roll call, overrode the mayor's vetoes of about $9 million in the new $1.6 billion budget and sustained him on about $1 million.

The overide of the mayor's vetoes was recommended by council chairman Sterling Tucker, a likely rival Washington in next year's Democratic primary for mayor.

In deliberating on the mayor's proposed 1979 budget, the council removed a total of $15 million. The mayor, in his veto message, asked the Council to restore $10.1 million.

After the council refused yesterday to do so, the mayor issued a statement saying the actions mean that "the citizens . . . can no longer be assured of the maintenance of critical services" in several departments, including Human Resources, Environmental Services and Transportation.

Yesterday's council action was final. The budget, as amended, now goes to the White House for submission to Congress early in 1978.