Mayor Harold Washington called a special City Council meeting today on short notice and, in a new rebuff to his authority, almost no one came.

Only 18 of 50 aldermen showed up, eight short of the required majority of 26, forcing the mayor to adjourn the session without considering his proposal that organizers of Chicago's major summer festival pay the city's costs of directing traffic and policing it.

The financially strapped city traditionally has absorbed the cost of helping to police ChicagoFest, a music, entertainment, food and arts event that usually attracts about 500,000 people daily. This year's festival begins Aug. 10 and continues through Aug. 24, with police costs estimated at $700,000.

Washington said the city, which has a $59 million deficit, according to its budget director, should be paid for its expenses. ChicagoFest is privately run and handled through the Chicago Park District, a powerful public agency independent of City Hall.

Washington said he will resubmit his resolution at a council meeting next week, and at a later news conference he said the city would provide police protection for the public. But the damage to his image seemed inescapable as several of his council allies filed glumly out of chambers after all but two of the opposing majority of 29 aldermen refused to attend.

Alderman Edward Burke, a principal opponent of the mayor, said he thought his colleagues had stayed away "because it's a beautiful day for golf."

Although Washington early in his administration boycotted several council meetings, this was the first time the majority aldermen used the same tactic on the mayor. The maneuvering and contention dates to Washington's first day in office, when 29 white aldermen seized control of the council and ousted Washington's supporters from important committee chairs. The factions have been at loggerheads ever since.

In an interview before the aborted meeting, Washington, who is black and a Democrat, traced the continuing confrontation to the struggle for power between the Democratic machine politicans and himself. Race, he said, "is a factor. The negative attitudes about race are used to tie this thing the opposition together. It's wrapped up in power and glued together with race."

In recent days, several white aldermen, including Roman Pucinski, a former congressman, have criticized the selection of finalists for chief of police because there are two blacks and a Hispanic but no white.

Despite the seemingly endless wrangling, Washington said he is firmly in control of Chicago. "We're runnning this government," he said. "The City Council has moved on everything of importance. All in all, I'm comfortable with our progress."

Washington said his first priority is to establish financial solvency "at least through 1984." He has proposed reinstating a $22 million property-tax hike. And 569 city employes will be dismissed by next month. The council majority opposes the tax hike and layoffs, but Washington vowed anew today to fire 2,000 city workers beginning Aug. 17 if he does not get approval of the new revenue bill.

The next most pressing matter, he said, is to "bring in the kind of leadership we need to keep Chicago solvent. We need economic growth, fair and equitable distribution of city services, and the people to run them."

He acknowledged that months of important labor negotiations lie ahead. Contracts with transit, fire, and police employes all expire by the end of the year but, he said, as an example of the systematic approach to administration he hopes to fashion, all labor negotiations will be conducted through a chief negotiator, not the mayor. "The mayor can't be running down every five minutes making public statements about the talks."

With the city strapped for cash, Washington indicated that there isn't much to offer the unions in the way of pay increases. One of his first acts as mayor was to rule out a promised $7.5 million retroactive increase for many of the city's 40,000 workers.

He said, however, that he did not expect the talks to be especially tough. "Based on my experience with organized labor in this city, I don't think they're going to spend all their time beating the bejeebers out of the mayor. They're going to sit down at the bargaining table having the advantage of a full and complete audit. They are going to know where every city dollar is and where it's going so there won't be any hidden tricks. They can't claim bad faith because they'll have all the facts."

Washington has conducted "town meetings" in two of the city's 90 separate ethnic neighborhoods, and said he will continue at a pace of one a month. Although many important executive jobs remain to be filled, Washington claimed that "so far we have brought in more women, blacks and Hispanics than you can count together over the past 15 years."