The District of Columbia's proposal to build a $110 million convention center in downtown Washington won strong and possibly crucial support yesterday from the two senior members of the House District Appropriations Subcommittee.

Statements at a public hearing by Rep. William H. Natcher (D-Ky.), the subcommittee's chairman, and Rep. Clair W. Burguner (R-Calif.), its top-ranking minority member, could set the House on a collision course with the Senate over the project.

Sen. Patrick J. Leahy (D-Vt.), chairman of the Senate District Appropriations Subcommittee, voiced skepticism at a hearing on the center's financing two weeks ago. An aide said yesterday that Leahy's position is unchanged.

In its pending budget for ifscal 1973, which must be approved by Congress, the city is seeking to borrow $27.7 million from Congress to design and start buying land for the project. the site occupies three blocks facing New York Avenue between 9th and 11th Streets NW, in the seedy Mount Vernon Square area.

Yesterday's House hearing was totally favorable to the convention center, with Mayor Walter E. Washington and other city officials testifying that the District is losing is attractiveness to major conventions because the city lacks a large auditorium with space for displays and exhibits.

Washington said the American Bankers Association, with draws 12,000 to its annual convention, and the National Association of Broadcasters, which draws up to 14,000 have said they will not return unless an adequate convention center is erected here.

City officials expect the facility to draw between 310,000 and 390,000 convention delegates each year. They testified yesterday that the center would continue to benefit the city financially even if attendance were to fall as low was 175,000.

Critics of the center will be heard today along with business spokesmen who support the plan.

Before yesterday, Natcher had expressed carefully hedged support for the convention center, reversing his opposition to a somewhat similar proposal that was advanced in 1973 but never approved.

Yesterday he said he was concerned whether the facility acutally can be built for its estimated cost of $110 million. Sam D. Starobin, D.C. director of general services, assured him it could. Natcher voiced satisfaction.

At the Senate hearing, witnesses for the U.S. General Accounting Office testified that the District government has a good record of completing construction projects within cost estimates.

As for the center itself. Natcher said yesterday that "it will produce benefits" for the city in terms of increased business, taxes and jobs. "We have a need for it," he said, adding later:

:"Here in Washington, we need some good news . . . some of the good news should incorporate and encompass a civic (convention) center."

Burguner said he agreed with Natcher and with city officials that the center's operations need not show a profit to produce an economic boon for the city through increased "spin oil" development and increased taxes.

By the city's own estimate, it will cost $8.4 million a year by 1984 to pay off the center's construction debt and another $500,000 to provide direct operating subsidies.

With the center generating an estimated $21 million annually in tax benefits as a result of related business activity, the city hopes for a profit of $12 million. Critics have challenged these projections as too optimistic.

Both lawmakers advised city officials to be conservative in projecting benefits. Burguner said House members have long memories and seem sure to compare the convention center project with the costly John F. Kennedy Center for the Performing Arts and the National Visitor CCenter at Union Station, although neither were built by the District government.

Del. Walter E. Fauntroy (D-D.C.) also testified yesterday in support of the convention center.

The one nongovermental witness heard yesterday, Richard G. Hanson, a Houston land development executive, testified that the convention center would spur redevelopment in the urban renewal area created by the city around the Metro Center station at 12th and G Streets NW.

Two hotel firms are interested in locating on some of the land in the urban renewal area, he said. They are Marriott and Radisson, whose interest in locating hotels in the area was disclosed at the Senate hearing two weeks ago.

City officials said two other hotel firms also have expressed interest in sites in the same area.