The statement purporting to be from a group called Ansar al-Islam -- or "Supporters of Islam" -- also said one of its leaders, Emad al-Din Abdel Hamid, was killed in Egyptian air strikes after the ambush.
The statement could not be independently verified.
No other group has claimed responsibility for the attack on police last month that saw assailants gun down officers in a shootout between Cairo and the Bahariya oasis in the Western Desert, a rare flare-up outside Egypt's Sinai Peninsula.
Egyptian police have for years been seeking a militant named Emad al-Din Abdel Hamid, a former military officer turned jihadist.
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He is believed to have joined a fellow officer, Hisham el-Ashmawy, in Libya following the 2013 military ouster of Islamist president Mohamed Morsi.
Ashmawy, who split with an Egyptian jihadist group that claimed allegiance to the Islamic State group in 2014, is thought to be aligned with Al-Qaida.
Egypt believes the militants have been plotting attacks from the jihadist stronghold of Derna in Libya.
Authorities are fighting against the Egyptian branch of the Islamic State group in the north of the Sinai peninsula, over 500 kilometres away from the scene of the October ambush.