D.C. Council member Betty Ann Kane, in her first major campaign statement on race, invoked the memory of John F. Kennedy and the success of blacks and whites during the civil rights struggle as proof that black voters will support her campaign for mayor of the District of Columbia, a predominantly black city.

"We all sometimes hear someone ask can Betty Ann Kane, who is not black, who is white, be elected mayor of the District of Columbia and how will she govern if elected," Kane told about 50 people attending a prayer breakfast at Zion Baptist Church of Eastland Gardens in far Northeast Washington.

"Here from our common bond is our answer," she said, and cited a 1960 speech by Kennedy to a group of Protestant ministers in Houston where he answered the question of whether a Roman Catholic could be president by saying that religion was not an issue in the campaign.

"Because I am a Catholic and no Catholic has ever been elected president, the real issues in this campaign have been obscured," Kennedy said then.

"To paraphrase Kennedy," Kane said yesterday, "Because I am white and no white has ever been elected mayor of Washington since home rule, the real issues of this campaign have been obscured."

Later Kane added, "I have great faith in our intelligence and sophistication as voters in our willingess and ability to look at all candidates and choose the person who we judge most qualified to represent us as mayor. The District needs a mayor whose public acts are responsible to all of its citizens and obligated to none."

Kane and her supporters said she chose to speak out on the issue of race yesterday because she is having difficulty convincing potential financial contributors and volunteers--particularly whites--that as the only white in a field of seven contenders she can win in a city that is 70 percent black.

Early election polls have shown Kane, twice elected an at-large member of the school board and in 1978 an at-large member of the council, in third place among candidates in the Sept. 14 Democratic primary.

She is far behind the top two candidates, incumbent Marion Barry and former Carter administration cabinet member Patricia Roberts Harris. She received 7 percent of the vote in the poll, and was the choice of 4 percent of the black voters polled, and 13 percent of the whites.

"There is a lot of white guilt that we have to overcome," said Bob Boyd, former executive director of D.C. Citizens for Better Public Education and a cochairman of Kane's campaign. "We hear it most from whites who say she can't win because she is white."

"Black voters are more sophisticated about the race question than whites right now," Boyd added. "She is mainly trying to answer the white liberals who don't know what kind of support she has among blacks who think there should be a black mayor for symbolism in a mostly black city. It's a silent issue on people's minds and its hurting us to just leave it there, so she is addressing it directly."

A gospel singer sang before and after Kane spoke and four black ministers sat beside her on the stage. But later all but one of the ministers said they were not supporting Kane.

"Some of her supporters live around here and I gave them the benefit of using the church, and that's all," said the Rev. Leon C. Collins, pastor of the church where the breakfast was held. "I don't care to comment on who I am supporting at this time but I'll tell you this. I'm not partial to color when I'm looking at people. It's the quality of the person that attracts me."

The Rev. A. Stanley Kenlaw, associate pastor at First Rising Mount Zion Baptist Church in Shaw, said he would support Kane. "This is a new day. There is no difference between black, green or white. She's talking about education, administration and organization. She has the know-how and the background to do a fine job."

One of Kane's supporters at the breakfast was Minnie S. Woodson, former president of the D.C. school board, who said that when she tells her friends she is supporting a white candidate for mayor they stop talking and then say, "Oh."

"Black people have so ingrained themselves that since the city is mostly black they definitely want to keep the reins of the governmnent in the hands of black people," she said.

"We've had no home rule in this city and we've had poor home rule with the two mayors we have had. We've never had the best. It's time to get the best leadership regardless of race," Woodson said.

Kane, holding a prayerbook and hymnal, said during the speech that there are common bonds between blacks and whites who struggled together during the civil rights movement. "In our city our common bonds are being tested--being challenged," she said.

Kane promised that if elected, she would pursue a vigorous affirmative action program in city government and work to get more Washington residents hired into white-collar jobs in downtown office buildings where many jobs now are filled by suburbanites.

"I don't understand why in this city where we have a program at the University of the District of Columbia to train young people to be nurses," Kane said, "the head of nursing at D.C. General says she has to go to the Philippines to recruit nurses."

"There is something wrong," she said, "when we have a summer jobs program, with 17,000 jobs and only 300 of those jobs are in the private sector . . . I will work to make sure the private sector hires our young people."