The arrests of several officials suggests Fifa is a "deeply flawed and corrupt organisation", the Culture Secretary has said.
John Whittingdale told MPs that Sepp Blatter should quit as Fifa president to give the organisation the fresh leadership it "very badly needed" in light of the scandal.
He said yesterday's events were "shocking in both their scope and scale" but they were also "far from surprising".
"This is the latest sorry episode that suggests that Fifa is a deeply flawed and corrupt organisation," he said in response to an urgent question on the issue.
He also called on sponsors to review their contracts with the organisation and to consider following Visa's lead in threatening to sever ties.
Vladimir Putin has accused the United States of meddling after senior Fifa officials were arrested on suspicion of corruption following an investigation by the FBI.
Russian officials said yesterday that the country's 2018 World Cup bid was fully compliant after Swiss authorities said they were investigating allegations of "criminal mismanagement and money laundering" in connection with the awarding of the tournament.
Attacking the corruption investigation into Fifa, Mr Putin said: "This is yet another blatant attempt (by the United States) to extend its jurisdiction to other states.
He said the arrests were a "clear attempt" to prevent the re-election of Fifa president head Sepp Blatter, who he said had Russia's backing.
FA chairman Greg Dyke has told ITV News "there's no chance" of England getting the chance to host either the 2018 or 2022 World Cups after Swiss authorities launched criminal proceedings into the allocation of the tournaments.
Embattled Fifa president Sepp Blatter has withdrawn from another scheduled appearance as the crisis engulfing his organisation continued.
Mr Blatter was due to give a speech at Fifa's medical conference at a Zurich hotel on Thursday morning, but the governing body said the 79-year-old would not be attending.
Blatter missed two meetings yesterday after senior officials were arrested on bribery and corruption charges.
The president - who is bidding to be re-elected at Friday's presidential election - issued a statement saying he was committed to removing those involved in corrupt practices from the game.
Fifa is facing a battle to keep World Cup sponsorship deals after several senior officials were arrested on suspicion of corruption.Read the full story ›
It "would make sense" to delay Friday's planned vote to elect a new Fifa president in light of the latest scandal to hit the organisation, France's foreign minister has said.
Laurent Fabius said Fifa currently had a "disastrous image" and time was needed to establish the facts.
"It's been several years that there have been accusations of corruption. It would make sense to take a bit of time, see what is true and not and then the authorities can adjudicate, but for now, it's giving a disastrous image," Fabius told a French radio station.
"I'm saying this on a personal level, but it would seem to make sense (to delay the election)," he said.
There is something "deeply wrong" at the heart of Fifa, Foreign Secretary Philip Hammond has said, as he became the latest figure to call for reform of the governing body.
"There is something deeply wrong at the heart of Fifa and international football needs to reform, needs to get its act together," Mr Hammond told the BBC.
He later told Sky News that a British politician in the same positon as Mr Blatter would be "struggling to cling on".
Nebraska became the first conservative state in more than 40 years to abolish the death penalty on Wednesday when lawmakers boldly voted 30-19 to override the governor's veto.
Conservative and Liberal politicians came together in an unlikely alliance after Republican governor Pete Ricketts attempted to veto a popular repeal bill.
Nebraska is the first Republican controlled state in the U.S. to abolish capital punishment since North Dakota did so in 1973.
The state had 10 inmates on death row, and hadn't executed anyone since 1997. It is the 19th state to abolish capital punishment.
The US Department of Justice has outlined 12 schemes it alleges the Fifa officials and executives arrested yesterday were involved with, dating as far back as 1993.
Payments and kickbacks are alleged to have been made during the organisation of various cup competitions, including the Copa Americas, the Copa Libertadores and the Copa Do Brazil in South America, the Concacaf Gold Cup and Champions League - decades' worth of World Cup Qualifiers in the Caribbean and Central America.
Votes on the host of the 2010 World Cup are also called into question, as is the 2011 Fifa presidential election, and kit supplies for the Brazilian FA.
Hundreds of millions of dollars are alleged to have changed hands across the various schemes.