Stockholm - Lennart Johansson, who lost to Sepp Blatter in 1998 FIFA presidential election, says the 79-year-old Swiss official should not delay his departure.
The election for a new president is not expected to take place until at least December.
"He must go immediately," Johansson said on Friday.
"People want us to be clean. You're seeing when he turned up at any match they were booing him. They really showed they were not satisfied."
Blatter said he would stand down as president on Tuesday, only four days after winning a fifth term amid criminal investigations into FIFA executives.
"I think the investigation going on has told him that they will find out exactly what was done and by whom," said Johansson, a former UEFA president.Meanwhile FIFA corrected its own statement about the previously secret payment five years ago to the Irish soccer federation.
FIFA originally said it was a $5m loan that was written off, but now the governing body says it was €5m.