Washington was one of six cities selected yesterday as a potential site for the 1988 Democratic National Convention after Mayor Marion Barry assured party members that his administration is "ready and willing" to handle the transportation, safety and housing demands posed by the event.

The 56 members of the party's site selection committee also voted unanimously to consider Atlanta, Houston, Kansas City, Mo., New Orleans and New York City.

The bids of Detroit and of Brook Park, a Cleveland suburb, were rejected by committee members because they did not meet certain technical requirements.

The committee members plan to start visiting the eligible cities in mid-September, when they will be subjected to "intense lobbying and wining and dining" by their hopeful hosts, said Terry Michael, a spokesman for the Democratic National Committee. A decision is expected by Jan. 1, Michael said.

Hosting the convention brings a city national exposure and a net profit as much as$15 million for the local economy, according to estimates from the 1984 convention in San Francisco.

The Democratic National Committee expects about 35,000 delegates, journalists and politicians in 1988.

The committee chose the six finalists after spending two days listening to proposals presented in terms of square-footage and numbers of hotel rooms. They pondered the floor plans of eight convention centers and the maps of eight public transportation systems as city officials enumerated the particular virtues of their respective locations.

Making Washington's bid yesterday morning, Barry said that the city, which came in second in the competition in 1984, was "the logical choice" for the convention: convenient, politically viable and a bargain to boot.

Flanked by the flags of Maryland, Virginia and the District, Barry said that a Washington convention would have the support of three Democratic administrations: his own, and those of Maryland Gov. Harry Hughes and Virginia Gov. Gerald L. Baliles.

At the heart of Barry's proposal was the claim that a convention would "cost $9 million less in Washington, D.C., than in any competing city." That reflects savings in hotel and transportation costs for party staff, delegates and their families, candidates, reporters and lobbyists who live and work here, he said.

These savings, which Barry called the"$9 million advantage," would mean that the Democratic Party would have more money to spend on the presidential race, he said.

To support his claim that Washington can handle large conventions, Barry cited the area's 40,000 hotel rooms, three airports and $87 million Washington Convention Center.

D.C. Police Chief Maurice T. Turner Jr. said that, of the 3,880 officers on the city's police force, at least 1,243 would be assigned full time to convention security. Preliminary figures show that the city's cost for hosting the convention would total $13 million.

Some observers have said that the Democrats should hold their convention in Atlanta or New Orleans, in order to attract southern voters who have been disenchanted with the party. Barry rejected that notion, saying that Washington would provide "the bridge between North and South because we are neither North nor South."

Nathan Landow, a Bethesda developer who is chairman of the Democrats' site selection committee, said that political considerations had not affected the committee's decision. He acknowledged, however, that politics "will come in at some point."