The 79-year-old Swiss held an emergency meeting with key Fifa officials on Thursday after world football’s governing body was subjected to yet more damaging corruption claims.
Platini then made a personal appeal for Blatter to quit but was told it was “too late” to resign.
Sepp Blatter: “I cannot monitor everyone all of the time… those who are corrupt in football are in a minority”
Blatter later vowed to restore trust in Fifa and “find a way to fix things”.
Opening a meeting of Fifa’s congress on the eve of Friday’s presidential election, he said: “These are unprecedented and difficult times for Fifa.
“It must fall to me to uphold responsibility for the well-being of the organisation.”
However, while admitting he could not be held responsible for the actions of a few, he conceded: “I’m sure more bad news may follow but it’s necessary to restore trust in our organisation.”
His speech came just hours after Frenchman Platini said the latest crisis had left him “absolutely sickened”, adding: “People have had enough, they don’t want this president any more.”
Blatter, who has been president since 1998, is seeking a fifth term when he takes on Prince Ali bin al-Hussein in Friday’s election.
Several influential football figures had called for the vote to be delayed after seven Fifa officials were arrested in Zurich on Wednesday.
But Uefa, which governs European football, decided on Thursday not to boycott the election and will continue to back Prince Ali, although some member associations, such as Russia, have said they will back Blatter.
Uefa head Michel Platini: “Blatter will convince the majority to vote for him… but he has already lost, Fifa has already lost”
Caf, which looks after the interests of Africa, has also reiterated its support for Blatter.
So has the Asian Football Confederation, although one of its members, the Australian football federation, has announced its intention to vote for Prince Ali.
“A big, big, big majority of the European associations will vote for Prince Ali,” said Platini.
Dutch FA boss and former presidential candidate Michael van Praag – who pulled out of the running so as not to split the anti-Blatter vote – said:
“He is the end responsible person in Fifa. You cannot always continue washing your hands.”
Fifa was plunged into fresh crisis on Wednesday when United States authorities indicted 14 people and arrested seven senior football officials on bribery and racketeering charges.
In a separate development, Swiss officials opening criminal proceedings into the bidding process for the 2018 and 2022 World Cup bid processes.
Blatter’s decision to chair an emergency meeting with representatives from Fifa’s six confederations is significant.
Jeffrey Webb, president of the North, Central American and Caribbean Association (Concacaf), and Eugenio Figueredo, president of the South American confederation, were both absent after being arrested on Wednesday.
Concacaf later said it had provisionally suspended Webb and president of the Costa Rican Football Federation Eduardo Li, who was also among the 14 indicted by US authorities.