The Chicago school board and the Justice Department reached tentative agreement yesterday to desegregate the nation's third largest school system next fall, but the species of how that would be done were left undecided until well after the Nov. 4 presidential election.

The preliminary settlemnt of this explosive issue climaxed more than a decade of battles between the federal government and Chicago that have featured periodic threats of lawsuits and the cutoff of federal school aid.

Justic gave the Chicago school board until March to come up with a detailed desegregation plan and appeared to play down the need for busing as a remedy for the school system, which is almost totally segregated. Instead, the department suggested the board might redraw attendance zones and attempt voluntary measures such as establishing special schools to attract interested black and white pupils.

Tentative settlement of this politically charged issue comes as President Carter is locked in a tight battle with Ronald Reagan for Illinois votes. While Carter is comfortably ahead in the heavily Democratic Chicago area, according to recent polls, he needs every vote in a state he lost to the Republicans by slightly fewer than 100,000 votes four years ago.

A Justice spokesman said the department had moved as rapidly as it could without regard to presidential politics.

The NAACP reacted angrily to the settlement, -- complaining that it had been excluded from the negotiations and criticizing the agreement for failing to set specific standards for a desegregation plan.

"An elephant labored and produced a mouse," said Thomas I. Atkins, general counsel for the NAACP. "In the absence of substantive content [to the agreement], the timing becomes suspect."

"It's a non-event. It builds up hopes for a [final] settlement when one is unlikely," said another civil rights observer.

The agreement set no required racial quotas and said that in cases where busing might be necessary, no pupil should be transported for a time or distance that would affect health or "impinge on the educational process."

"More important than creating racial balance at every school is the demonstration that the system has desegregated to the maximum extent feasible and has eliminated state-maintained black or white schools in favor of 'just schools,'" Justice said.

The department said it intends to conduct an investigation of Chicago's largely white suburban school districts and might later seek to include them in an overall metropolitan desegregation plan.

The battle with Chicago's schools stretches back to the 1960s, a time when the Rev. Martin Luther King Jr. said he found their segregation more contemptible than the racism he had encountered in the Deep South.

The federal government found that over the years Chicago had gerrymandered school attendance zones to perpetuate segregation. It had also used mobile classrooms at overcrowed black schools and failed to send black children from even the most crowded black schools to underutilized white schools.

Federal officials found that the school board had bused 300 children out of a severely overcrowded black South Side school to another all-black school four miles away. A largely white school sat less than two miles away with six empty classrooms.

Federal efforts to pressure Chicago to desegregate began in the Johnson administration but over the years, Chicago's potent political machines have been able to resist. Francis Keppel, federal commissioner of education in the 1960s, has recalled that when he tried to withhold federal funds to force Chicago to desegregate, an outraged Mayor Richard J. Daley wasted little time getting to the White House. The funds were not withheld.

Not much was done in the Nixon and Ford administrations but the efforts were resumed in the Carter administration by Joseph Califano's Department of Health, Education and Welfare, and were continuing when he left. Almost immediately, Califano's chief civil rights enforcer, David Tatel, became embattled with the new department secretary, Patricia Roberts Harris, who dressed him down for not showing "political sensitivity."

Tatel and the Chicago board wrangled without resolving differences. Then Chicago School Superintendent Joseph P. Hannon pushed a totally voluntary plan called "Access to Excellence" that resembled some of the suggestions in yesterday's decree. Tatel demanded that the school system come up with a plan under which no school would be more than 50 percent white. The Chicago board refused. Last October, Secretary Harris referred the case to the Justice Department.

Two weeks ago, as Chicago School Board member Joyce Hughes and the Justice Department were winding up the negotiations, Mayor Jane Byrne spoke to a community group in al all-white neighborhood of southwest Chicago.

"I think you'll be happy with the settlement," she told them. "There is no cause for fear on behalf of your children, your livelihoods or your neighborhoods. I am quite confident of that."

There are about 460,000 pupils in Chicago's public schools. About 61 percent are black, 18 percent white, 19 percent Hispanic and 2 percent Asian.

According to a federal government survey a couple of years ago, 80 percent of the city's elementary pupils attended schools that were either 95 percent black or 95 percent white.

The school system is in serious financial straits, said this caused the state legislature to pass a bill last winter ousting the predominantly white school board with which HEW had negotiated. In May, Byrne appointed a new, predominantly black and Hispanic board which conducted most of the negotiations leading to yesterday's agreement.

A Justice spokesman characterized those negotiations as cooperative. The school board's Hughes, a Northwestern University law professorr, had been a longtime friend of Assistant Attorney General Drew Days and "they were able to hit it off," the spokesman said. Hughes and Days are black.

Days, personally handling the final details of the settlement, flew to Chicago yesterday for a rare court appearance. He filed both a suit formally charging the Chicago school system with discrimination and the consent decree that the city school board and Justice Department signed.

In March the board must file its detailed plan. There could be hearings and a court order if Justice objects to it.

Attorney General Benjamin Civiletti urged his department to attempt to reach a negotiated settlement and avoid a court battle, particularly because of the serious financial problems of the Chicago school system.

Civil rights observers complained yesterday that the issue over which Tatel and the Chicago board fought is still unresolved in yesterday's agreement and any desegregation specifics are postponed until March when the school board is to file its formal plan.

"What they have done is agree to plan," said the NAACP's Atkins. "Hell, they could have done that 10 months ago."

"I think people should wait and see what the plan is before they shoot it down," said a spokesman for Justice's Civil Rights Division.