Zurich - 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 Friday. "People want us to be clean. You are seeing when he turned up at any match they were booing him. They really showed they were not satisfied."
Also read: Critics want FIFA boss Blatter out now
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.
1225 GMT (8:25 a.m. EDT)
FIFA has corrected its own statement about the previously secret payment five years ago to the Irish soccer federation.
FIFA originally said it was a $5 million loan that was written off, but now the governing body says it was 5 million euros ($7.1 million in January 2010).
1030 GMT (6:30 a.m. EDT)
The head of the German soccer federation says FIFA should not have given $5 million to Ireland to silence complaints about the handball which led to the country missing out on the 2010 World Cup.
FIFA only disclosed the payment on Thursday.
FIFA and the Irish soccer federation had not previously mentioned the deal, which came after a World Cup playoff in 2009 when Thierry Henry's handball led to France's winning goal.
German soccer federation president Wolfgang Niersbach told ZDF television on Friday that the handball "was a real injustice" and accepted the Irish were "outraged."
But Niersbach says "you cannot compensate it with money and no court would have ruled in their favor."
1005 GMT (6:05 a.m. EDT)
The president of the influential German soccer federation, Wolfgang Niersbach, says a new FIFA president needs to be elected sooner rather than later.
"For me it's incredible the way it happened. You (Sepp Blatter) invite the whole world to a congress, you get re-elected and then four days later you resign, for whatever reason, but it's not an immediate resignation," Niersbach told German TV station ZDF.
FIFA said four months are needed to set up the extraordinary congress to elect the new president but Niersbach said "everything needs to go much faster."
0935 GMT (5:35 a.m. EDT)
FIFA President Sepp Blatter will not attend an Olympic meeting next week in Lausanne, Switzerland.
Blatter, who has been an IOC member since 1999, was invited to Tuesday's briefing for members by the 2022 Winter Games bidding candidates.
FIFA says Blatter already told the IOC in April he would not be attending and "his plans have not changed."
As the head of a summer sports federation, Blatter is less committed to attend an event involving 2022 bidders Beijing and Almaty, Kazakhstan.
Still, Blatter would be expected to attend the host city vote on July 31 in Kuala Lumpur, Malaysia.
FIFA has not confirmed travel plans for Blatter since an American federal investigation of corruption in soccer erupted last week.