Football Association chief Martin Glenn has apologised "for any offence" after comparing the Star of David with symbols such as the Nazi swastika.
Glenn was discussing Manchester City's Spanish manager Pep Guardiola, who has been wearing a yellow ribbon in support of imprisoned politicians in Catalonia.
He said "we don't want" the Jewish Star of David, swastika, or ex-Zimbabwe leader Robert Mugabe on a shirt.
The Jewish Leadership Council said the comparison was "offensive".
The Star of David is on Israel's flag, their national team shirt and FA logo.
Responding to the apology on Monday, the JLC chief executive Simon Johnson said he had spoken to Glenn and "explained why his comments caused such serious offence".
He continued: "Martin apologised, explained the context for his comments and stated that he did not intend to cause offence, which I accepted. I have thanked the FA for their apology and I am glad that this has been dealt with swiftly."
As part of his apology, Glenn agreed with the JLC that the Star of David "is a hugely important symbol to Jewish people all over the world".
Anti-discrimination body Kick it Out said it welcomed Glenn's apology.
In a statement to BBC Sport prior to Glenn's apology, Johnson said: "I have no problem with the FA clarifying Rule Four and specifying that all religious symbols are prohibited on a kit, if that is the case.
"In explaining that decision, the chief executive's examples are ill-judged and in poor taste.
"The Star of David is a Jewish religious symbol of immense importance to Jews worldwide. To put it in the same bracket as the swastika and (former Zimbabwe leader) Robert Mugabe is offensive and inappropriate."
Last month, the FA charged Guardiola over his decision to wear the ribbon.
"You can't have, and we don't want, football equipment to display political symbols," said Glenn.
"To be very clear, his yellow ribbon is a political symbol, it's a symbol of Catalan independence.
"We have re-written Law Four of the game so that things like a poppy are OK.
"But things that are going to be highly divisive, and that could be strong religious symbols - it could be the Star of David, it could the hammer and sickle, it could be a swastika, anything like Robert Mugabe on your shirt - these are the things we don't want."
The former Barcelona coach was given two formal warnings about the issue in December before being charged by the FA in February.
He has until 18:00 GMT on 5 March to respond to a charge of breaching kit and advertising regulations.