Al-Qaeda-inspired Ansar Beit al-Maqdis accused Israel of pressuring Cairo to wage a "war on Islam and Muslims in Egypt, particularly in the Sinai... To protect (Israeli) security."
Since the Egyptian military overthrew Mohamed Morsi in July, the interim authorities have carried out a bloody crackdown on the Islamist former president's Muslim Brotherhood.
And militant attacks in north Sinai have killed scores of Egyptian soldiers and police.
The army has poured troops into the mountainous and underdeveloped Sinai Peninsula, which borders the Palestinian Gaza Strip and Israel, to combat the growing militancy.
More From This Section
In September, Ansar Beit al-Maqdis carried out a suicide bomb attack on the Egyptian interior minister's motorcade in Cairo, which the official survived.
On Monday, an Israeli security source said at least one rocket was fired at Eilat. News website Ynet said two rockets exploded in the early evening without causing casualties.
And last month, the group claimed a car bomb attack in northern Egypt that killed 15 people, mostly police.