Gianni Infantino has scrapped a plan to sell shares in a company that would run the commercial and operational aspects of competitions including the men's and women's World Cups, after a backlash from confederations.
The proposal was rejected by three continental confederations, with Uefa warning that its nations would boycott Fifa events if it went ahead.
Proposal dropped
Mr Infantino said early on Saturday that "this proposal will not proceed" after it became clear the project had "created divisions".
In a statement, he said: "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."
Andy Burnham called the plans "outrageous", saying they made clear Mr Infantino was "the wrong man to lead the organisation".
Opposition within Fifa
The plan also provoked high-level opposition inside Fifa. Senior adviser Carlos Cordeiro resigned, and chief operating officer Kevin Lamour described the project as "a project of one person".
Uefa vice president Laura McAllister said trust in the Fifa president had been "badly shaken" and Uefa would be "considering options". It is not clear whether the U-turn will alleviate pressure over his position.
Questions over leadership
She told BBC Radio 4's Today programme: "I think trust in the president of Fifa has been badly shaken this week, without a doubt, and I think quite rightly, people will ask questions about whether he is the leader to take us forward as a global football organisation."
Asked whether Uefa might find a challenger to stand against Mr Infantino, she said all confederations would be considering options, but added: "I think it's early days yet." She stopped short of saying Mr Infantino should resign.
She later said: "Interestingly, I don't think the sport of football is damaged by what's happened this week. I think Fifa as an organisation, is, and I think the president is."
