FIFA's senior vice-president, Julio Grondona, has accused England of "always complaining" and said he voted for Qatar for 2022 because "a vote for the US would be like a vote for England".
Reports had been published in the English press accusing FIFA of corruption ahead of the 2018 and 2022 World Cup votes, and former FA chairman Lord Triesman made a series of accusations against four FIFA executive members last month.
Current FA chairman David Bernstein has most recently led a bid to delay the FIFA presidential elections in which Sepp Blatter stands unopposed in the wake of the current crisis.
Grondona, president of the Argentinian FA and head of FIFA's finance committee, said: "We always have attacks from England which are mostly lies with the support of journalism which is more busy lying than telling the truth. This upsets and disturbs the FIFA family.
"To present such a project as David Bernstein presented is like shooting a penalty because it cannot be always from the same place that the insults and problems come from.
"I see it at every Congress. They have specific privileges with four countries having one vice-president. I don't know what our president has said, but we have seen the World Cup go around the world, to South America and Africa and it looks like this country does not like it.
"It looks like England is always complaining so please I say will you leave the FIFA family alone, and when you speak, speak with truth."
In an interview with a German press agency on Tuesday, Grondona called England "pirates" and added: "Yes, I voted for Qatar, because a vote for the US would be like a vote for England, and that is not possible.
"But with the English bid I said: Let us be brief. If you give back the Falkland Islands, which belong to us, you will get my vote. They then became sad and left."