Culture Secretary John Whittingdale says the credibility of FIFA president Sepp Blatter has been "utterly destroyed".
He told the House of Commons that the Government stood behind the Football Association's efforts to end the culture of "kickbacks and corruption" in the game.
It comes after seven senior FIFA officials were arrested last week in Zurich on a US warrant connected to a bribery scandal.
He said: "FIFA's voting system is designed to support the incumbent and it returned a predictable result, but there is no doubt that what remained of Sepp Blatter's credibility has been utterly destroyed."
He added: "For the good of the game, it is time for Sepp Blatter to go."
Shadow culture secretary Chris Bryant said: "Sepp Blatter survived last Friday thanks to his Mafioso cronyism, but he is the tainted leader of a corrupt organisation and by clinging on he is merely dragging FIFA further and further into the mud."
He suggested setting up a rival competition in both 2018 and 2022 - the years in which Russia and Qatar respectively are due to the host the World Cup.
He suggested that more should be done by UK authorities to investigate, asking: "Why is it that the pioneering investigative reporting of the Sunday Times and Panorama has been left to one side, and it's only the US and the Swiss that have been taking the lead on prosecutions."
Mr Whittingdale responded that an alternative world football competition could only be done with the support of other major footballing nations.
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