The Tawheed and Jihad group also mourned the leader of an armed Palestinian faction, a top lieutenant and three other members who died in an Israeli air strike on Thursday that also killed a nine-year-old Palestinian boy.
Israel has blamed a Palestinian faction, the Popular Resistance Committees (PRC), for the attacks along its border with Egypt. Within hours of the assault, the Israeli airforce struck back at the PRC, which is based in Gaza, killing five of its members.
"We in the Tawheed and Jihad group bless these blessed arms that pounded the fortifications of the vendeta-filled Jewish enemy in the so-called Eilat area in southern occupied Palestine," the group said in a statement posted on the Internet.
It said the attack had sent Israel and "their border guards in the Egyptian army" a message that Egypt has joined the struggle against what it called the enemies of God.
Israel said the gunmen who carried out the triple attack near the Red Sea resort of Eilat had come from Gaza through neighbouring Egypt, a charge denied by Hamas.
Israeli aircraft struck Hamas security installations in Gaza on Friday, killing at least one Palestinian, in further retaliation for attacks along the Egyptian border.