Sepp Blatter admitted the events of this week "unleashed a storm" ahead of the 65th FIFA congress in Zurich but appealed to delegates for unity.
The FIFA presidential election went to second round of voting after neither candidate gets required two-thirds of votes. Blatter received 133 votes, but he needed 140 to pass. Prince Ali garnered 73.
Blatter, 79, is facing Prince Ali Bin Al Hussein of Jordan in the FIFA presidential election on Friday. In Blatter's opening remarks, he said there had been a question mark over the congress taking place.
Blatter addressed FIFA's 209 members hours before the vote in which he is a seeking a fifth term. He has refused calls to resign after FIFA was targeted by U.S. and Swiss authorities in separate corruption investigations.
Both Blatter and his rival, Prince Ali, were allotted 15 minutes to address the delegates just prior to the vote. Voting was done over secret paper ballots in alphabetical order at two special booths set up at each end of the venue.
"We don't need revolutions, but we always need evolution," Blatter said during his pre-vote speech. "Yesterday, the day before and today, I am being held accountable for the current storm. OK, so be it. I will shoulder that responsibility. Just as I said, I will take it upon myself. I will accept it and I want to fix FIFA together with you.
"I want to hand over a FIFA that will have emerged from the storm. A FIFA that will have enough safeguards which will not need the political interventions. I promise you this," Blatter said.
Prince Ali, meanwhile, promised to unify and restore credibility to football's governing body during his address to the delegates.
"The eyes of the world are upon us and not for the first time. But this time, everything is at stake. For the game -- for the world," Prince Ali said in his speech. "We are guardians of the game, a game that is cherished by the world. A game that can unite and heal. About men and women who give their all and who inspire the youth."
"We stand here today at a crossroads for football and a strong leader is needed to fix the mess we are in. I will stand as that," the Jordanian delegate said. "We want transparency, inclusiveness and accountability. Everyone pulling in the same direction for the good of FIFA and football."
In agenda items leading up to the vote, the Palestinian FA dropped a motion to have Israel suspended from FIFA, with an amended proposal being voted through the FIFA congress by 90 percent on Friday.
The presidents of PFA and Israel FA shook hands following the vote.
Also, Swiss police said a bomb threat was made against the venue where the FIFA congress is being held.
Zurich city police spokesman Peter Sahli says a police operation is ongoing but declined to provide further details.
An AP reporter at the scene says the Hallenstadion's concert hall auditorium was cleared but the building itself was not evacuated. FIFA secretary general Jerome Valcke said "an anonymous threat against the FIFA congress was received.'' The meeting then resumed after lunch.
FIFA also announced that the post-congress news conference will take place on Saturday morning.
In his opening remarks to FIFA delegates, Blatter said: "The events of this week unleashed a storm.
"It was even questioned whether this congress would go ahead but I am appealing for unity and team spirit to tackle the problems that have been created and to solve them.
"It will not be done in a single day, it will take some time.
"The important point today is to move ahead -- and the important point is transparency. We have a problem to solve."
Blatter claimed that FIFA's crisis would not have happened if countries other than Russia and Qatar had won the vote for the 2018 and 2022 World Cups.
Most of the media investigations into FIFA have come from Britain, while fourteen current and former FIFA executives and associates were indicted on an array of charges by the U.S. Department of Justice.
In what appeared to be a reference to the U.S. and England losing out on their bids to host World Cups, Blatter said: "If two other countries had emerged from the envelope I think we may not have these problems. But we can't go back in time, we're not prophets, we can't say what would have happened."
The meeting in Zurich was briefly disrupted by two protesters who unfurled a Palestinian flag -- the Palestinian Football Association has demanded Israel be kicked out of FIFA -- before they were removed by security.
The president seeking re-election from the 209 associations in Friday's vote despite calls from UEFA president Michel Platini to step down.
FIFA ethics judge Hans-Joachim Eckert told kicker he was not surprised by the recent developments before the FIFA congress.
In November 2014, Eckert, the chairman of the adjudicatory chamber of FIFA's independent ethics committee, released a 42-page report on the investigation into the bidding processes for the 2018 and 2022 World Cups.
It cleared Russia and Qatar of corruption in their winning bids for the two upcoming World Cups.
The full Garcia report has yet to be published in full, with the FIFA announcing on Wednesday that it will eventually be fully disclosed at an unnamed point in the future.
Already in December, the FIFA executive committee voted during a meeting in Marrakesh, Morocco, to fully disclose the report.
"I was not surprised by the actions taken, because, in November 2014, FIFA handed over the documents of the report to the Federal Public Prosecutor in Bern with the request for examination whether to open investigations," Eckert said.
Eckert's summary of the 430-page Garcia report into the bidding process led to a fallout between the German judge and former U.S. Attorney Michael Garcia, with the latter claiming the summary was "incomplete and erroneous," and later stepping down from his role as FIFA ethics investigator.
In events leading up to the election, FIFA delegate Iesha Johansen of Sierra Leone gave a moving statement of thanks to Blatter, the English football delegation and others for their financial and emotional support as her nation struggled to fight the world's worst-ever outbreak of Ebola.
"Football is more than just a game, it is about bringing people together," she told delegates Friday. "We all need to give peace a chance.''
More than 11,000 people have died since the Ebola epidemic emerged in Guinea in December 2013. Guinea and Sierra Leone are now the only West African countries still reporting new Ebola cases.
ESPN FC correspondent Stephan Uersfeld and The Associated Press contributed to this report.