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Blatter's comments mark a reversal for the FIFA president. At the FIFA congress meeting in Hungary in May, Blatter had led a standing ovation for the ailing 96-year-old Brazilian Havelange.
But Blatter has been under mounting pressure since last week after Fifa released a Swiss prosecutor's report confirming Havelange accepted kickbacks from marketing agency ISL in the 1990s.
"He has to go. He can't remain honorary president after these incidents," Blatter told Swiss weekly SonntagsBlick in an interview that was published on Sunday.
Blatter was a senior official during Havelange's reign at FIFA. The 76-year-old Blatter, who is Swiss, took over from Havelange in 1998.
He had previously acknowledged that he knew about payments, but insisted they were legal in Switzerland at the time.
"I only learned of it (the payments), after the collapse of the ISL agency in 2001," Blatter said. "It was FIFA which made a criminal complaint at the time and thereby got the ball rolling in the ISL case."
FIFA has been shaken by a scandal, including over allegations of vote-rigging when football officials awarded the 2018 and 2022 World Cup hosting rights to Russia and Qatar, respectively.
On Friday, the head of Germany's football league, Reinhard Rauball, called on Blatter to resign over corruption allegations.
Blatter has insisted he does not condone bribery and told the newspaper he could run for another term in 2015.
"Let's see how my health is," he told the paper. "I've just been for a checkup and I lost four kilograms (eight pounds)."
Last year, Blatter was elected for a fourth, four-year term as FIFA president. He was the only candidate.
