“Our heroes became martyrs during their jihadist mission against the Jews,” said the statement, which named the four men, members of a Sinai tribe.
At a funeral Saturday, four bodies were draped in black flags with scripture from the Koran, according to photos from the scene.
Neither Israeli nor Egyptian military officials have asserted responsibility for the attack.
Egyptian security officials, speaking to the Associated Press on the condition of anonymity, said that a drone firing from the Israeli side of the border had killed five, not four, suspected militants.
The officials said the Israeli strike was coordinated with Egypt, which would mark an advance in the often-clandestine partnership between the two militaries.
An Egyptian military spokesman, Col. Ahmed Mohammed Ali, said the army was investigating two explosions in the area. He denied that there was any attack on Egyptian soil launched from Israel. “The claim that there is coordination between the Egyptian and Israeli sides concerning this subject is completely wrong,” he said.
A tribal leader in the area, Abdel Karim, said in an interview, “Don’t believe the Egyptian television. They are all liars. The planes came from across the border. They came and they fired, then they left.”
The online statement from the jihadist group, whose source could not be verified, accused the Egyptian army of working with the Israelis. “What kind of announced betrayal is bigger than this? For the Egyptian army to allow the Zionist unmanned airplanes to breach its borders repetitively.”
Spokesmen for the Israel Defense Forces declined to comment on the incident. Israeli military officials say their unmanned vehicles do not carry offensive weapons.