Grondona, the senior of FIFA's six vice-presidents and the president of the Argentina FA, called the English "liars" and "pirates" at the FIFA Congress in Zurich in June, but Bernstein told the Leaders in Football conference in London that he had received a letter of apology from him, retracting his remarks.
Bernstein told delegates: "I was pleased to receive a letter of apology from the Argentinian (FA) president Grondona following his unacceptable comments about England in Zurich."
Grondona's comments came after Bernstein had asked Congress delegates to postpone the FIFA presidential election on June 1, where Sepp Blatter was elected unopposed.
The situation arose after then Asian football chief Mohamed Bin Hammam, who was due to stand against Blatter, withdrew his candidature following bribery allegations.
Bernstein revealed on Wednesday that on the morning of the vote more than 50 delegates from UEFA tried to persuade him not to go ahead with his plan, but he insisted it was the right thing to do.
After Bernstein spoke at the Congress, Grondona launched his attack.
The Argentinian told the Congress: "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.
"I see it at every Congress. They have specific privileges with four countries having one vice-president.
"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 earlier on the same day, Grondona told German reporters that England were "pirates" and added: "With the English [failed 2018 World Cup] 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."
Bernstein, also told delegates that England's relationships with FIFA and UEFA were improving, but said he was "not holding his breath" regarding planned FIFA reforms due to be announced later this month.
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