Quinn's reaction came a day after several Chicago aldermen defended Burris, saying he has not been accused of any wrongdoing, and issued a warning.
Burris was appointed to the seat by Rod Blagojevich after the former governor's December arrest on federal corruption charges for, among other things, allegedly trying to sell the appointment. Several lawmakers, including Quinn and U.S. Sen. Richard Durbin, have called on Burris to resign after more revelations about Burris' attempts to raise money for Blagojevich while lobbying his inner circle.
Quinn said he feared the controversy surrounding Burris would echo the "Council Wars" of the 1980s, when race divided the city's Democrats.
Congressman Danny Davis of Chicago said there's considerable support in the black community to leave Burris "alone and let him do his job." He decried the aldermanic comments as "divisive," but said those calling for Burris' resignation are "overreaching."
The Burris defense, which continues with a rally by ministers Saturday, comes after the senator brought on political consultant Delmarie Cobb amid a controversy that threatens his political future.
Also Friday, Burris' attorney, Timothy Wright, sent a letter to Atty. Gen. Lisa Madigan warning of a fight if lawmakers and Quinn try to dislodge Burris from office by approving a special election for his Senate seat.
Tribune reporters Rick Pearson, Hal Dardick and Ashley Rueff contributed to this report.