The City Council formally requested yesterday that Mayor Dennis J. Kucinich resign. The action was a prerequisite for setting the first recall election in the city's history, a vote that could come between Aug. 2 and 22.

The 31-year-old mayor, who abandoned his legal fight against the recall when the Ohio Supreme Court declined to hear his case Thursday, refused to resign and said, "Bring on the recall." Kucinich's lawyers had unsuccessfully argued that some signatures on the recall peitions were invalid because the signers had not voted in the 1977 municipal election. The signatures were formally certified at a hastily called special City Council meeting at 8:00 A.M. yesterday.

Kucinich unveiled bumper stickers that had been prepared before the council's action yesterday that read "Support Kucinich, the Peoples' Mayor."

"Let's tell the whole country once and for all that Clevelanders run their city government," Kuninich said at a news conference. "Not the party bosses, not the council leaders, not certain corrupt big business interests, not organized crime, but the people of Cleveland run Cleveland."

It was an indication that Kucinich had already geared up for a campaign as enthusiastic as the one he ran last year in winning election as one of the nation's youngest mayors.

Barring any unforeseen developments, this would be the first recall election of a big city mayor in the nation since July 1975 when then Seattle Mayor Wesley Uhlman crushed a recall attempt led by that city's firefighters. Uhlman picked up 63.2 percent of the vote, a better showing than his 52 percent majority when he won reelection in 1973.

The recall drive against Uhlman was launched after he fired the city's fire chief. The campaign to oust Kucinich began in March when he unceremoniously fired Police Chief Richard D. Hongisto, the former San Francisco sheriff, during a prime time news conference on Good Friday.

Hongisto's firing angered Clevelanders and spawned the formation of The Recall Committee to Save Cleveland, which collected 39,500 ballot signatures.

If Kucinich does not resign, as he has vowed not to do, the council must set a special election between 40 and 60 days from yesterday.

Contributing to the serious political crisis in this city are separate recall drives against nine of Cleveland's 33 councilmen launched in past weeks by grass-roots organizations.

Several of the targets are councilmen backing the Kucinich recall drive. They have accused Kucinich of spearheading the drive from behind the scenes, a charge Kucinich has denied.

Should enough signatures be collected against the councilmen, their seats could be on the ballot along with Kucinich's.

In addition, there is a campaign underway for a referendum to reduce Kucinich's salary from $50,000 to $20,000 and the councilmen's from $18,500 to $2,000. If 5,000 signatures are collected for this change, it too could be on the August ballot.

Describing this sudden wave do-it-yourself government in Cleveland, one officeholder said, "the people in Cleveland are just fed up with government, like everyone else in the country, and they want to handle this one their own way," said a Cleveland office holder in a reference to all of the referenda.