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The Australian, speaking at a sponsor's event in July, talked about how disappointed he was by his team's Six Nations loss to the "scummy Irish" and described Wales as a "s*** little place".
"No excuses. I shouldn't have said what I did," Jones told the BBC. "I am very sorry for any offence caused."
The English RFU said it would apologise to the sport's ruling bodies in Ireland and Wales, and a spokesperson described Jones's comments as "inappropriate".
England, whose defeat by Ireland last year was their first under Jones, play the Irish in this year's tournament at Twickenham on Saturday.
Ireland will complete the grand slam for the third time if they beat England, who won the Six Nations for the last two years but have lost to Scotland and France in the past month.