District of Columbia City Council member Marion Barry and lawyer John L. Ray, two self-described "underdogs" in the Sept. 12 Democratic mayoral primary, have each raised far more money in campaign funds than has City Council Chairman Sterling Tucker, who is believed by many to be the front-runner in the race.

Barry, aided by six donations of $1,000 each, hae received $10,695 in campaign contributions, according to reports filed this week with the D.C. Board of Elections and Ethics.

Ray, the 34-year-old former Senate staff lawyer who last October became the first announced candidate for the post, has raised $6.250, according to the report. Of that amount, $3,000 is a loan from a Houston businessman and another $1,525 came from others who live outside the Washington metropolitan area.

Tucker reported raising $2,830, including one $1,000 contribution from lawyer Donald Brown and two contributions of $500 each from lawyer Ralph Emerson and George Jones, a Northwest Washington physician.

While Ray's formal candidacy is nearly four months old, Tucker and Barry have been announced candidates for only about three weeks. That short span of time, the fact that the election is eight months away and the still uncertain status of the incumbent, Mayor Walter E. Washington, would appear to limit the impact of the early fund-raising totals.

The lists of contributors also indicated that realtors, developers, abankers, lawyers and utility and retail executives - the major source of funds for political campaigns in; the city- have not yet begun to give in large amounts.

The amounts reported this week could also be misleading because most of the candidates - Barry, Tucker and Washington in particular - have, for months, been lining up pledges of financial support from many business people who have yet to send in their contributions.

Still, both Ray and Barry were quick to attach significance yesterday to their suns in proportion to Tucker's. "it shows we have to be taken seriously, more seriously than some of the political leaders would have you believe," Barry said.

"it tells you what a lot of people are thinking," Ray said. "They don't want Walter Washington. They don't want Sterling Tucker. They don't want Marion Barry. They want a new face."

Gerald Wallette, Tucker's campaign manager, said, "I'm not the least bit distressed that John Ray has raised twice as much as us and Marion has raised three times as much. It's too early to tell if that's an indication of anyone's fund-raising capacity over the longer haul."

Sam Eastman, Walter Washington's press secretary, said the mayor was not raising any campaign funds and, to Eastman's knowledge, no one else is raising campaign money on Washington's behalf.

The filing of the reports comes at a time when a fifth poll of voter opinions has shown Tucker to be the most popular candidate, and also given some potentially ominous information about two possible races of City Council.

Aro-American Datanamics, a Northwest Washington firm, surveyed last week 403 city Democrats who said they intend to vote in the September primary. Of that total, 27 percent said they would vote for Tucker, 18 percnet were for Barry, 16 percent for Washington, 37 percent undecided and the remainder scattered among various other possible candidates.

Because the poll had a 7 percent margin of error, and a relatively high number of undecided voters - more than one of every three - its strongest indication was that the race is wide open. Ray's name was not included in the sample.

Late last year, in a poll of 1,000 registered city voters, the firm found 21 percent of Washington, 14 percent for Tucker and 11 percent favoring Barry. There were 36 percent undecided and the rest in favor of a host of other perons.

Because the first Datanamics poll asked and open-ended question, some polling experts considered it primarily a test of name recognition. Datanomics president Milton White said yesterday such as interpretation could be valid.

White said the findings of the second Datanamics poll indicated a "fluid" situation. "If an election were held tomorrow, the poll's very, very accurate. As a predictor of what will happen in September, it's accurate only to the extent that something sensational doesn't come along to change the electorate's mind."

The three other polls - one each by Barry supporters, Tucker supporters and The Washington Post - have shown Tucker to be the most popular mayoral candidate. In addition to oneitting Ray, none of the polls have included Charles Suel (Trummie) Cain, a far Southwest Washington teacher who says he is also running for mayor.

Ronald H. Brown, chairman of the board of the University of the District of Columbia, also is contemplating running for mayor, but has been largely ignored in most of the polls taken thus far.