Six challengers for seats on the D.C. Council yesterday sought to boost a petition drive for a proposed initiative that is intended to increase spending for the city's public schools.

Organizers of the effort said that in the past five weeks they have gathered 5,000 of the 13,800 signatures needed to put the initiative on the November ballot, and described the promised support from the candidates as crucial. The signatures must be delivered to the Board of Elections and Ethics by July 7.

"At this moment, we have a less than a 50-50 chance of getting enough signatures, but we're still going to try," said Roderic Boggs, director of the Washington Lawyers Committee for Civil Rights, which represents Parents United for D.C. Schools, the principal group involved in the initiative effort. "Support from the candidates . . . gives the issue prominence in the campaign and it puts people out there gathering signatures."

If approved by voters, the initiative would declare as public policy that public education is "of the highest priority" in the District and that the school board budget should reflect that policy. It would also require that public hearings be held before the Board of Education can present its budget request to the mayor and again before the mayor presents his recommendation to the council.

Boggs said he believes the hearings will generate the kind of public pressure that Parents United created earlier this year when it organized a protest in front of the District Building in support of funding increases for teacher salaries, books and supplies and building repairs.

School board members complained loudly about the mayor's initial fiscal 1987 budget proposal for the schools, and Superintendent Floretta D. McKenzie threatened to resign unless more funds were budgeted. The council later approved a budget of $393.8 million, larger than that proposed by the mayor. However, school officials said more money is needed to help students achieve academic excellence.

D.C. schools have more dilapidated school buildings and fewer books, and spend less money per pupil than many nearby suburban school districts, according to a recent study by Parents United.

The six challengers for council seats announced their support at a news conference at the Adams Elementary School, 19th and California streets NW. The news conference was attended by council member Hilda Mason (Statehood-At Large), who previously declared her support for the initiative, school board member Eugene Kinlow, Washington Teachers Union President Harold Fisher and members of Parents United.

Jim Nathanson, a public school teacher and a Democratic candidate for the Ward 3 seat on the council, said, "I've already given 10 petitions to initiative backers . I challenge other candidates to double that, which is what I plan to do." Harry Thomas, a Democratic candidate for the Ward 5 council seat held by Democrat William Spaulding, said, "The initiative is the voice of the people. Sometimes it's the only avenue for the grass-roots people to make their voices heard."

Others endorsing the initiative were Ruth Dixon, Mary Draper Janney and Mark Plotkin, candidates for the Ward 3 seat, and Bernard Gray of Ward 6. All are Democrats.