Ansar Beit al-Maqdis, which has spearheaded an insurgency in Egypt's restive Sinai Peninsula, made the claim in a video posted on social media.
The group has killed scores of policemen and soldiers since the army overthrew president Mohamed Morsi last year, but the October 24 attack in which a jihadist rammed a military checkpoint in northern Sinai with an explosives-packed car was the deadliest such incident in years.
It said it was acting in retaliation for a crackdown on Islamist supporters following Morsi's removal from power.
At least 1,400 people have been killed in the crackdown, while more than 15,000 have been jailed and hundreds sentenced to death.
In the video, the group promises further attacks against the security forces and said it was speaking directly to President Abdel Fattah al-Sisi, the former army chief who toppled Morsi and unleashed a crackdown on Islamists.
Earlier this week, Ansar Beit al-Maqdis pledged its allegiance to the Islamic State organisation in Iraq and Syria in a bid to boost recruitment and bolster its fight against the Egyptian army, according to analysts.
