Being a Republican in the District of Columbia "is not as lonely as you might think," suggests a top GOP official here as his party wages a spirited but little noticed mayoral primary campaign.

The two candidates in the Sept. 12 Republican contest, Arthur Fletcher and Jackson Champion, confidently predict that party labels will not matter that much in the general election two months later, particularly if the Democratic opponent is incumbent Mayor Walter E. Washington.

Mismanagement of city government will be the dominant Republican theme no matter with Democrat wins the primary, and the candidates say they expect this issue to offset the considerable election handicap of looking for votes in a town with 181,000 registered Democrats and only about 21,000 registered Republicans.

City Republicans used to number some 40,000 eligible voters but party officials say registration began to drop dramatically about five years ago - during the Watergate scandal - and has leveled off only in the past couple of years.

"I'll need a lot of luck, prayers and some money," said Fletcher, a former Labor Department official and presidential adviser, who sees osme indication that the mismanagement issue is drawing support from Democrats.

Flethcer's opponent, Champion, runs a publishing business out of his home and is making his second try at becoming the District's first elected Republican mayor in the 20th century.

Champion's election battle, however, is being fought as much against the leadership of the D.C. Republican party - which has endorsed Fletcher - as against the city's Democratic administration.

Both candidates agree that incumbent Democrats "have made a mess of things" in the District and that Mayor Washington, the man most clearly associated with city government, will make the best political target in the general election.

"When this city administration talks about this being a boom town and still the youth of the city are unempolyed, you know there's mismanagement," said Champion, 55. "It's a case where they (Democrats) have promised, promised, promised, promised, but they have not delivered."

Fletcher, 53, considered the front-runner in the primary race, said he fears serious consequences - here and nationwide - if city government services do not improve.

"The issue is the ability of the D.C. Government, Particularty the executive branch, to deliver quality of life services to the people," Fletcher said.

But another issue, in his view, is the image of black self-government that has been projected since the District received home rule.

"The D.C. government is very important in the minds of blacks around the country," said Fletcher. "We should do as excellent, superb job of managing the city, not half manage it. We've got to manage our funds and government now, and in this city . . . it's bad to get this opportunity and then fumble like we are."

Fletcher said he has ecountered "a seething anger, really a kind of hopelessness" among voters when they talk about city government services.

Still he acknowledged, the inital response to his candidacy is: "A Republican mayor? You've go t to be kidding."

But Republicanism may not be the chief concern of the voters in the Nov. 7 election, according to Paul Hays, chairman of the D.C. Republican Party since 1976 and one of Fletcher's strongest supporters.

"Walter Washington is without question the strongest campaigner in the Democratic race," said hays. "Unfortunately, his administrative abilities don't meet the same standard."

Four years ago, said Hays, the Republican Party did not actively oppose Mayor Washington. The mayor won easily with 79,605 votes to only 3,501 for Jackson Champion.

Hays predicted it will be a much closer election this fall if Washington and Fletcher go against each other, but he said voter "dissatisfaction with the incumbent administration" encompasses the mayor's two principle Democratic challengers, City Council Chairman Sterling Tucker and at large Councilman Marion Barry.

Most of the city's Republican voters live in the relatively affluent Northwest neighborhoods of Ward 3, which is predominantly white, and Ward 4, predominantly black. But party officials say they do not have an exact racial breakdown of the membership.

So far Fletcher has raised about $16,000 in political contributions, much of it from the D.C. party, Republican Congressmen and national party officials he met during the Nixon and Ford administrations, when he was assistant secretary of Labor, alternate U.S. representative to the United Nations and, later, a White House urban affairs adviser.

In sharp contrast, Champion said he intends to spread no more than $250 in his election race and as not sought contributions.

At the Labour Department, Fletcher developed the controversial "Philadelphia Plan" to increase minority employment in federal government construction projects around the country. in between jobs with Republican administrations, Fletcher was executive director of the United Negro College Fund and, more recently, operated a private consulting firm.

As a younger man, Fletcher was active in Republican politics in Washington state and served on the Pasco, Wash., city council. A self-help business project he started there is credited with influening Richard Nixon's ideas about black capitalism and bringing Fletcher to the attention of the national party.

Champion is a native of South Carolina but grew up in New Rochelle, N.Y. He was once publisher of a small community newspaper and later gave up a successful sales agency job to start a national weekly paper, the Grass Roots, designed to encourage development of minority businesses. He is a past member, by presidential appointment, of the board that over-saw operation of the former Washington Technical Institute.

Making much of his previous involvement in D.C. Republican politics, Champion has accused Fletcher of being an outsider. He has also continued to allege, as he did four years ago, that the city Republican Party structure is "racist" because it "denies people the opportunity to participate" in party affairs.

Fletcher said Champion's failure to win his local party's backing in 1974 "is his problem, not mine," but he admitted his lack of prior in-depth involvement in city politics will likely be an issue in the general election.

"What we have in D.C. is a management problem," said Fletcher, who added that corporation and cities using the city manager system of government recruit around the country for the best person to fill the job. "If longterm residency were the answer (to managing the city), why do we have the problem"?

If elected mayor Champion said he would release "all the land and housing swallowed up by the old Redevelopment Land Agency" and allow citizens, especially those displaced by redevelopment, to homestead the property. He also supports restricting city employment to D.C. residents, would attempt to "force" unions to accept affrimative action programs and would like to legaline gambling here. He, like Fletcher, would want a reference or the proposal to build a downtown convention center.

Fletcher said he hopes to sharpes the focus on such issues as housing, economic development and tax limitation by "debating them publicly with whomever in the Democratic candidate in November."

And "instead of hiring a political helpmate to be city administrator," said Fletcher, clearly referring to Mayor Washington's longtime friend and confident, city administrator Julian Dugas, "I will hire me a city manager who has been trained to understand urban problems."

Champion and Fletcher agreed that the upcoming bribery trial of farmer mayoral aide Joseph Yeldell could be an important election issue. But Fletcher said he does not expect the trial scheduled for Oct. 2, to get under way before the November election "if Mayor Washington wins the primary. Some lawyer will get sick or something."

The two candidates said their strength is coming from Democrats as well as Republicans "who are saying they want change" and are looking to the two-party system to bring back competition in District government affairs.

The lopsided registration figures make it hard for a D.C. Republian to challenge a Democreat, admitted Fletcher, but he insisted that "an issues-oriented" campaign this fall will change all that.

"Let the candidates talk about what they're going to do, not what they've done," said Fletcher, adding that the mayor should do more in his campaign" than take credit for keeping the city calm" after the 1968 riots here.

"That was a legitimate claim, but what have you done for us lately?" Fletcher said. "The issues of the 1960s is not what the future's about. If that's all he can offer, he's served his purpose and needs to move on."