The group, calling itself the Mujahedeen Shura Council of Jerusalem, made the claim in a video distributed in Gaza on Tuesday.
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The short video identifies two men, one Egyptian and one Saudi, as the perpetrators of Monday's attack. The men, speaking in front of an al-Qaeda flag, say they are about to carry out a "double suicide mission."
In Monday's attack, two terrorists crossed into Israel from Egypt and killed an Israeli civilian working on the border fence. They were then shot dead by Israeli security forces.
The authenticity of the video could not be verified. Israel has warned that al-Qaeda-inspired groups now operate in Gaza.
Israeli officials declined comment.
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