Blatter — who faces a reelection vote Friday — opened Fifa's annual congress by saying he could not be blamed for the corruption controversy which even drew Russia's President Vladimir Putin and British Prime Minister David Cameron into the fray.
But after the arrest of seven top football officials at the Fifa hotel on Wednesday Blatter warned that the storm is not over.
"The next few months will not be easy for Fifa," the 79-year-old said.
"I am sure more bad news will follow but it is necessary to begin to restore trust in our organization," he said.
"We cannot allow the reputation of football and Fifa to be dragged through the mud any longer — it has to stop here," he added.
Blatter called the scandals "unprecedented" and said the "actions of individuals bring shame and humiliation on football and demand action and change from us all."
He spoke hours after a showdown with European football chief Michel Platini who called on Blatter to quit.
Platini said he confronted Blatter at an emergency meeting of the heads of the the six regional confederations.
The Uefa president said he was "sickened" and "disgusted" at the arrests and a raid by Swiss police on Fifa headquarters as part of a corruption inquiry into the awarding of the 2018 and 2022 World Cups to Russia and Qatar.
The seven arrested in Zurich are among 14 people accused by US authorities of taking more than $150 million in bribes.
"Today I have come to ask you to quit Fifa, to resign from Fifa, to leave Fifa because its image is bad and we can no longer go on like this," Platini said he told Blatter in front of the other presidents.
Blatter only replied in a private conversation after. "He told me: 'Michel we know each other well, but it's too late. I cannot leave today when the congress starts this afternoon."
Blatter remained defiant despite mounting pressure over the scandals.
Credit card giant Visa said it would "reassess" its sponsorship if Fifa does not clean up the sport.
Unless Fifa rebuilds a corporate culture with "strong ethical practices" at its heart, "we have informed them that we will reassess our sponsorship," Visa said.
Coca-Cola, Adidas, McDonald's and Budweiser also spoke out against the corruption scandal.
Even International Olympic Committee president Thomas Bach said in front of Blatter that Fifa must change.
"I would very much like to encourage you to continue and strengthen your co-operation with the relevant authorities to shed full light on the concerned methods and to take all necessary measures to address such grave allegations," Bach told the Fifa opening ceremony.
Blatter has not been personally implicated in the scandals and Swiss authorities said there were no immediate plans to question him.
And the spotlight now moves to Friday's vote when Blatter remains the favourite to extend his 17-year-old rule over the world's most popular sport.
Uefa had called for Friday's vote to be postponed because of the corruption arrests. But other regional groups said it should go ahead and Uefa said it would not boycott the vote.
Platini said that a "very, very, very large majority" of the 54 European nations would back Prince Ali bin al Hussein of Jordan, the Fifa vice president who is the only challenger to Blatter in the vote.
He called on other regions to back the prince. But African and Asian groups say they are still backing Blatter.
The seven arrested football officials — including Fifa vice presidents Jeffrey Webb and Eugenio Figueredo — remained in custody on Thursday.
Six have indicated they will fight extradition to the United States, Swiss authorities said.
Governments from around the world waded into the increasingly bitter and political battle.
'Attempt to block Blatter'
Russia's President Vladimir Putin slammed the Zurich arrests as a US attempt to oust Blatter.
"This is clearly an attempt to block the reelection of Blatter as president of Fifa and is an extremely serious breach of the principles of how international organizations work," Putin said, accusing the United States of trying to "spread its jurisdiction to other countries".
British leader Cameron backed calls by the English FA for Blatter to resign, his spokesman said.
South Africa meanwhile hit back at US claims in their indictments that South African officials paid $10 million in bribes to host the 2010 tournament. Some bribes were handed over in a briefcase stuffed with $10,000 bundles of cash.
"When we concluded the Fifa World Cup here in South Africa we got a clean audit report," said Minister in the Presidency Jeff Radebe, who was on the local organizing committee.
"There has never been any suggestion that anything untoward happened in South Africa."