FIFA should postpone Thursday's vote to choose the 2018 and 2022 World Cup hosts and allow an independent investigation into corruption allegations, watchdog body Transparency International (TI) said on Monday.
"FIFA's integrity and credibility, already shaken in the past, have been badly tarnished and the reputational damage suffered by FIFA these last weeks is considerable," the anti-corruption organisation's Swiss chapter said in a statement.
"It threatens to extend to other sports associations and to the whole of Switzerland which is their home and whose citizens often have key positions in them."
FIFA suspended two executive committee members earlier this month following allegations of wrongdoing in the Sunday Times newspaper.
A British Broadcasting Corporation (BBC) television programme on Monday accused three other FIFA executives of taking bribes.
TI, which issues a widely published and respected global league table of corruption, said: "The awarding of the 2018 and 2022 football World Cup, foreseen to take place on 2 December 2010, must be postponed until all light has been shed on the allegations published in the press.
"These have cast such discredit on FIFA's processes that a decision under these circumstances would only fan the controversy."
It said the internal investigation by FIFA's ethics committee, which resulted in the suspension of executive committee members Amos Adamu and Reynald Temarii, was inadequate.
"An investigation must be conducted by an independent body in order to establish the facts.
"FIFA's ethics committee does not seem to present the required degree of independence; furthermore, the body conducting the investigation must have extensive investigative powers in order to be able to establish the whole truth."
FIFA were not immediately available to comment.