successor," he said Tuesday.
Blatter did not say when the election would be held but said it should before the next World Congress in May 2016. It cannot be held for at least four months, according to FIFA rules, said Domenico Scala, chairman of FIFA's audit and compliance committee.
"The expectation is that this could take place anytime from December of this year to March of next year," he said.
Speaking in Zurich, Blatter said the reforms he has tried to implement over the years have not been enough.
"I felt compelled to stand for re-election, as I believed that this was the best thing for the organization. That election is over, but FIFA's challenges are not. FIFA needs a profound overhaul," he said.
He continued, "While I have a mandate from the membership of FIFA, I do not feel that I have a mandate from the entire world of football -- the fans, the players, the clubs, the people who live, breathe and love football as much as we all do at FIFA."
Michel Platini, president of UEFA, European soccer's governing body, has criticized Blatter in the past and told reporters last week that he had asked Blatter to bow out of the elections. He was one of the first to react to the announcement: "It was a difficult decision, a brave decision, and the right decision."
Read his entire speech
Blatter won a fifth term Friday despite a week marred by arrests, investigations in the United States and Switzerland and questions about whether he was the man to rebuild FIFA's reputation.
Blatter failed to get the required 140 votes in the first round of voting to prevail. Another round of voting was called, and because Blatter would need only a simple majority to win the second, his rival, Jordan's Prince Ali bin al-Hussein, conceded.
The prince would not say whether he is planning to run for the seat Blatter will vacate and said "I'm at the disposal of our national association. That's it." He later added that he was at the disposal of all of soccer's national associations "who want change," especially those who were afraid to voice concerns before Tuesday.
"I am always there to serve football and I think that is the most important thing. After this, I think we have to do so much work to fix this organization in a proper way," he said.
Asked his reaction to Blatter's annoucement, he replied, "It is the right move for Sepp Blatter, and I think we have to look to the future. ... We have to bring back FIFA to being a service organization."
The president of the embattled organization will continue his duties until a new president is elected, he said Tuesday.
Normally, the FIFA president is elected at the organization's World Congress, the next one being scheduled in Mexico City on May 13.
Waiting until then to elect new leadership "would create unnecessary delay and I will urge the executive committee to organize an extraordinary congress for the election of my successor at the earliest opportunity."
Who is Sepp Blatter?
As he won't be a candidate, he said, it will allow him "to focus on driving far-reaching, fundamental reforms that transcend our previous efforts. For years, we have worked hard to put in place administrative reforms, but it is plain to me that while these must continue, they are not enough.".
Among those reforms are "integrity checks" for all executive committee members, term limits for the president and executive committee members, and electing the executive committee members, Blatter said.
"I have fought for these changes before and, as everyone knows, my efforts have been blocked. This time, I will succeed," Blatter said.
Swiss authorities are questioning executive committee members as part of their probe into the 2018 and 2022 World Cup bids. Blatter is not being investigated as part of that probe, the Office of the Attorney General of Switzerland said in a statement.
Meanwhile, an investigation in the United States resulted in the FBI arresting nine FIFA officials and five corporate executives. The American investigation targets what one high-ranking IRS official called "the World Cup of fraud."
Blatter is not one of those arrested or facing charges by U.S. authorities, but he was among those investigated.
Asked if the U.S. investigation had cleared Blatter, Attorney General Loretta Lynch told reporters, "I'm not able to comment further on Mr. Blatter's status." Officials had said earlier that the investigation into Blatter's possible involvement continues.