Sixteen D.C. Republicans who helped nominate Ronald Reagan for president tried yesterday to establish their own ties with the incoming GOP administration by calling a press conference to tell Mayor Marion Barry that he would have to deal with the new White House through them.

The 16 delegates and alternates, who attended the July Republican convention committed to George Bush, before he released his delegates to vote for Reagan, have formed a new "Committee for a New Beginning," chaired by lawyer Melvin Burton. The committee, after its first meeting yesterday, declared that City Council member Jerry A. Moore Jr. (R-At Large) should be Barry's official liaison with the Reagan administration, and said Barry should channel all future White House contacts through Moore.

The mayor had no immediate comment.

Yesterday's announcement was the latest incident in an increasingly active political jousting match as D.C. Republicans try to make the most of the coming to town of a Republican president.

Long ignored in local decision-making and rarely consulted on mayoral or White House appointments, Republicans here are outnumbered by Democrats 9 to 1 among registered voters and have only one person among the top 15 elected officials in the city -- council member Moore.

Yesterday, they left no question that they hope to use their new access to the White House to bolster their minuscule party for future local elections and to promote loyal Republicans.

Burton said that Barry must go through Moore "for any audience that the mayor wants with the Reagan-Bush administration." The Republicans were angered by Barry's comments in an interview last week in which the mayor said he had ties to the Republican Party through his relationship with Sen. Charles McC. Mathias of Maryland, Dr. James Johnson, a former member of Reagan's California cabinet, and Elizabeth Dole, the wife of Sen. Bob Dole of Kansas and a key member of Reagan's transition team.

Arthur A. Fletcher, who chaired the Bush delegation to the convention and was Barry's unsuccessful 1978 Republican challenger, said that Barry must now understand that "one of the best ways to get his programs through a Senate controlled by Republicans and a White House controlled by a Republican is to work with local Republicans."

Fletcher said that Sen. Dole, who supported Fletcher's campaign for mayor and is now in line to head the Senate Finance Committee, "is going to be looking to see if Barry understands the need for working with us." The key component of the mayor's overall financial plan for the city, a proposal to borrow $215 million from the U.S. Treasury, could wind up in Dole's committee, and the implication was clear that the proposal would be in jeopardy without the support of the local Republicans who spoke yesterday.

The Republicans also announced the formation of a "truth squad" that will from time to time "issue papers and documents trying to counter any negative publicity being generated by the Democrats against this administration."

District Republicans once had considerable influence in city affairs but have seen it dwindle to almost nothing since the advent of limited home rule in 1975 and the election of a Democratic president in 1976.

Moore's seat on the council was virtually reserved by a charter provision prohibiting any one party, such as the powerful Democrats, from holding more than two of the council's four at-large seats. The other Republican elected official, school board member Carol Schwartz (Ward 3), was elected running in a nonpartisan race.

Burton said his committee will be preparing a list of qualified District residents for Reagan's transition team. "We shall look first for qualified people in the Republican party. If there are any positions left, we will be looking for independents and Democrats, and notice the order in which I said that."

The new president will be able to make appointments to the city's courts, to the Pennsylvania Avenue Development Corporatation and to the National Capial Planning Commission, among others.

"The Republican Party in the District is a viable party," Moore said. "We will now assert ourselves and become a viable force in the community."