"I wish that I had not made this off-the-cuff joke at the top of my remarks, and I apologize to anyone who was offended by it," said Jones, following his remarks to the Washington Institute for Near East Policy last Wednesday.
"It also distracted from the larger message I carried that day: that the United States' commitment to Israel's security is sacrosanct," Jones said in the statement.
The White House distributed a transcript of the speech by Jones, but there was no reference to the joke, which the national security advisor said was intended to "set the stage of my remarks."
It was the only moment of levity in the speech, which detailed US efforts to thwart Iran's nuclear program and to broker a resumption of talks between Israel and the Palestinians.
Abraham Foxman, national director of the Anti-Defamation League earlier told ABC News that the joke was "inappropriate."
"It's stereotypic. Some people believe they need to start a speech with a joke. This was about the worst kind of joke the head of the national security council could have told."
In the joke, as related by Jones, a Taliban militia member was parched and went to a Jewish vendor begging for water. But the vendor offered to sell him a tie instead.
Then the vendor told the militia member, he would forgive him for a tirade of slurs set off by the remark, and directed him to a nearby restaurant, where he could buy water.
A while later, the Taliban member came back fuming, telling the vendor "your brother tells me I need a tie to get into the restaurant."
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