But, despite walking back on his plans, UEFA has declared a loss of confidence in Infantino, with the Football Association supportive of the stance taken by European football's governing body.
FIFA had announced on Tuesday that it was seeking to launch FIFA Forward Enterprise (FFE), which would bring together the sale of FIFA's commercial rights - including broadcasting, sponsorship, ticketing and licensing - with the operational delivery of its tournaments.
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Infantino had then given football associations until September 19 to back his proposals to sell off part of FIFA to private investors with a £30.1m incentive to accept.
But the controversial proposals received fierce criticism from UEFA, CONCACAF (the North American, Central American and Caribbean association) and the Asian Football Confederation (AFC).
Prime Minister Andy Burnham adding his condemnation by calling for "FIFA to undertake an urgent review of its governance". On Saturday, he told Sky News FIFA's climbdown was "the right decision".
A statement from Infantino in the early hours of Saturday read: "The FIFA Forward Enterprise project was intended to provide a basis for further strengthening our FIFA member associations and our sport worldwide, especially in those countries where support is most needed.
"And more so, as we said from the outset, to do this only if a majority of the FIFA member associations were in support and always subject to a consultation process with them, the FIFA council, the confederations and wider stakeholders.
"Having listened carefully to all the views, it has become clear that the project has created divisions of a nature that, regardless of the level of support, are no longer in the interest of the objective set out in the first place. Our purpose has always been - and will always be - to unite and improve.
"As a result, this proposal will not proceed. Moving forward, my intent is to bring all interested parties back together in the coming days and weeks in the spirit of shared interest in our game, and with the objective to continue growing football everywhere, particularly in those countries that mostly need our support."
Writing on the AFC website, Sheikh Salman bin Ibrahim Al Khalifa welcomed FIFA's decision to abandon plans to sell a stake in the World Cup.
"Any initiative that has the potential to impact global football will be presented and discussed with the confederations, the FIFA council, member associations and other stakeholders in a timely, transparent and meaningful manner," he wrote.
"The future of global football must always be shaped through proper consultation, collective dialogue and respect for the established governance structures of our game."
'Approaching game over for Infantino'
Sky Sports News' Kaveh Solhekol:
"We have passed the tipping point and are approaching game over for Gianni Infantino. This whole disaster has been self-inflicted.
"There was no need for him to be in the situation he finds himself in today. He is now losing all his authority and his power. We have had statements from UEFA and other football associations.
"Reading between the lines, they are calling for Infantino to resign. They don't want to say it explicitly, no body wants to be the first [to say it].
"They are basically saying it is time to go and they no longer believe in him. This is one scandal too many, especially if you read UEFA's statement.
"They have basically said they have lost confidence in Infantino and to hold a review into what has gone on, with no options off the table.
"I think by saying no options are off the table, they are saying that they will look for somebody new to take over from Infantino.
"He has lost the support of the few backers he had left."
'The task of rebuilding trust in FIFA has only just begun'
UEFA welcomed FIFA's decision to abandon its plans, adding it would work with partners and stakeholders to ensure such moves cannot be fast-tracked without consultation in the future.
A UEFA statement read: "UEFA thanks all the fans, leagues, clubs, players, individuals, associations and confederations that opposed the scheme, alongside the many prime ministers, heads of state and commentators who have demonstrated to the FIFA president that football is not for sale.
"We cannot keep going on like this with secret schemes on fast-track timescales, cooked up by faceless individuals and of dubious benefit to the game. We must identify those responsible and hold them to account.
"It is right that, in the coming days and weeks, UEFA will work with its associations and in close cooperation with other confederations to reflect on how this happened and devise a plan to make sure that it cannot occur again.
"That review should be thorough and fundamental. No option should be off the table. The current FIFA leadership has not only lost UEFA's confidence but also that of many other members of the football family.
"When Gianni Infantino asked for the trust and the votes of FIFA's member associations to elect him as their president in 2016, he said, 'Of course we have to be transparent. I have been this in the last 15 years of my life in UEFA. You will have to play a part every day in the life of FIFA', before telling the assembled stakeholders, 'The money of FIFA is your money. It's not the money of the FIFA president. It's your money. You are the national associations and the money of FIFA has to serve for the development of football and not for anything else'.
"On both these promises, he has failed to deliver. The shabby, back-room, opaque deal he hatched and tried to force through was anything but transparent.
"And with reserves standing at over $5bn (£3.7bn), he has also failed to use associations' money for the benefit of the game.
"UEFA will begin work immediately with partners and stakeholders all over the world and right across the game to propose a new way of distributing resources through the existing FIFA Forward programme.
"We must start to use some of that money that is sat idle in FIFA's bank account to deliver the kickstart that the grassroots and the wider game need in each of the 211 countries of FIFA. But we don't need to sell off the family silver to pay for it.
"This is a victory for the whole game. But it must not be the end of the story. The proposal has gone. The task of rebuilding trust in FIFA has only just begun."
FA and FAW firmly behind UEFA
The Football Association has declared its unequivocal backing for the position taken by UEFA.
"We fully support UEFA's position," an FA statement read.
"It is time for a full and robust review of FIFA's leadership and governance to ensure that the global game is run transparently, for the benefit of all 211 member nations and with the long-term stewardship of football at its heart"
The FAW added: "The Football Association of Wales (FAW) supports UEFA's position regarding a robust review of the leadership and governance of FIFA.
"FIFA and its members are custodians of the game, responsible for its long-term growth, development and sustainability. This requires leadership that puts our game first in all of our decisions."
Sell-off plans condemned
Pressure increased on Infantino after Carlos Cordeiro, one of his senior advisors, resigned in protest at the privatisation plan, saying it was a "bad deal for football" and "for the long-term future of the game".
In an exclusive statement to Sky News, Cordeiro added: "As a senior advisor to the FIFA president, a former banker and a lifelong football fan, I cannot stand by while FIFA considers selling a stake in the World Cup.
"Let me be clear: I had no involvement in this proposal and I oppose it unequivocally."
A second FIFA official - chief operating officer Kevin Lamour - had also said the governing body's staff were "deceived" by Infantino's lack of openness over his plans, and told the Associated Press news agency that staff "deserve better than contempt and intimidation".
Lamour called the World Cup plans "the project of one person" and said it was time for football leaders to take action.
Cordeiro's resignation and Lamour's comments came after FIFA had released a statement in the early hours of Friday morning insisting "nobody is selling football" amid criticism of its proposals.
What were FIFA's World Cup plans?
Under the initial proposal to launch FIFA Forward Enterprise (FFE), football's world governing body aimed to raise up to $4.2bn (£3.1bn) from external investors through the sale of minority, non-controlling stakes in FFE, which it said would be valued at around $20bn (£15bn).
The governing body said its plans - which would have required approval from member associations - could deliver more than $10bn in "football development funding" over the next four years.
Who could replace Infantino?
Sky Sports News chief correspondent Kaveh Solhekol:
There's been talk about the president of Paris Saint-Germain, Nasser Al-Khelaifi, one of the most powerful men in world football, who is on the UEFA executive committee. But my understanding is that he is not interested in replacing Infantino.
Other candidates are people like Sheikh Salman bin Ibrahim Al Khalifa, who came second in the vote to become FIFA president 10 years ago. He's the president of the AFC, who also oppose the sell-off plans.
Then there's the president of CONCACAF, Victor Montagliani. We've just had the World Cup in three CONCACAF countries and historically, CONCACAF have been close to Infantino, but they said on Thursday that they rejected the proposal as well.
Finally, someone I think would be very popular is Aleksander Ceferin, the president of UEFA. He has a totally different vision about the way football should be run. If he was the president of FIFA, there would be no hydration breaks, no FIFA Peace Prizes, no Qatari-owned private jets for the president, no $1m (£742,000) World Cup tickets.
But I don't think Ceferin has ever expressed any desire or interest publicly to replace Infantino.
Perhaps we are getting ahead of ourselves. Infantino is under a lot of pressure and it would be fair to say he is fighting for his job, but we are not at the stage where people are going to come out and say they are going to stand against him.