Mayor Walter E. Washington entered the race to build the metropolitan area's first convention center yesterday when he announced plans for a mammoth, $110 million facility shortly before a rival center proposed for Prince George's County failed in an early crucial test before a legislative committee.

The mayor's proposal called for building the new center on the edge of the city's old downtown, near Mount Vernon Square NW, where District planning officials believe it will strengthen the city's tax base and rejuvenate what once was Washington's commercial heart.

At a press briefing yesterday afternoon, the mayor professed not to be worried about the rival center, announced by Prince George's a week ago and slated for a site near the Capital Centre in Largo.

But city officials were undoubtedly heartened later in the day when they learned that the Maryland House of Delegates Appropriations Committee voted against a $20 million bond issue to help finance the Prince George's County center. The bond issue was a key element of the county's plan.

The mayor's announcement culminated six months of intensive work by city planning officials and an outside consulting firm. The film prepared an elaborate report concluding that a convention center near Mount Vernon Square would be a boon to the city in terms of additional sales, hotel and property tax revenue - even though the center itself will need a subsidy of more than $8 million a year to break even.

The economic feasibility report, researched and written by Gladstone Associates, projects that a major convention center here with 300,000 square feet of exhibition space will draw 300,000 to 400,000 additional outertown conventioneers to the District once the facility opens in 1983.

In fact, Washington is already one of the nation's most popular convention cities. But, in recent years, it has been losing some of the largest annual group meetings because there is no exhibition hall here large enough to house the displays and tens of thousands of delegates who normally attend these large conventions.

The Gladstone report suggests that the additional conventioneers and exhibitors who will come to Washington after the center is built will spend an additional $100 million here - "outside" money that the District would not otherwise have.

"These expenditures will have an impact on many local businesses and individuals: for example," the report says, "$40 million in additional hotel room receipts, more than $30 million in new restaurant business and even 1 million additional taxi rides per year."

The 300,000 to 400,000 "new" conventioneers will create demand for an additional 3,000 hotel rooms in the city.The District can expect significant new sources of property tax revenues from the new hotels that would be built as well as other income from a nightly hotel occupancy tax that already exists.

The Mount Vernon Square site, one of 13 considered by the D.C. Municipal Planning Office, was selected because of its central location in the vicinity of New York Avenue and 11th Street NW, its proximity to two Metro stops and the availability of land nearby for anticipated construction of new hotels and office buildings.

Three different "schemes" were developed by Gladstone, architects and city planners as possible configurations for the proposed center. Each of the schemes called for a 300,000 square foot facility with 40 additional meeting rooms and about 25,000 square feet of storage facility for convention exhibits.

The designs differed, however, in their overall cost primarily because they required different amounts of land - which the city will have to buy from private owners.

The proposal that the mayor is expected to formally present next week to the City Council is the least expensive of the three but is still expected to cost $109.6 million by the time it is built.

The exact location of the center proposed by the mayor will be: "Ninth Street NW (to the east), Eleventh Street NW (to the west), New York Avenue NW (to the north) and H Street NW (to the south).

Unlike the Prince George's County proposal, which called for a combination of public and private financing, money to build the city's convention center would be borrowed entirely from the U.S. Treasury as part of the District capital budget.

The city would pay interest on this money for 30 years, although the Gladstone report suggests that the center could be refinanced soon after it is completed at a lower rate if the city is in a position by then to float its own general obligation bonds.

Debt service on the $110 million in borrowed money would total at least $7.6 million a year for 30 years. In addition, the center is expected to operate at a $600,000 annual loss. Nevertheless, the Gladstone report says the city can expect increased tax revenues directly attributable to the center of anywhere from $12 million to $14 million a year.

Civic leaders in Washington have been talking about building an exhibition hall in the city since at least the turn of the century. The old Auditorium Commission backed a convention center for the District in the 1950s.

A serious proposal was put forward in 1973 but was blocked by Rep. William H. Natcher (D-Ky.), chairman of the House District Appropriations Subcommittee, because city officials could not demonstrate to his satisfaction that the proposed Eisenhower center would benefit the city financially.

Natcher has since indicated, however, that he favors a convention center in the District - at least in principle. City government officials now believe they have a good chance of seeing a convention center started by 1979.

City Council Chairman Sterling Tucker, who attended the mayor's briefing yesterday, appeared to speak for all city officials present when he said: "This is a happy day." CAPTION: Picture, The major's plan for a $110 million convention center is shown in an architect's drawing.