Ansar Beit el-Maqdis, a Salafist extremist group that operates in the Sinai Peninsula and the Gaza Strip, claimed responsibility, Ynetnews.com reported.
"Our war against the enemy in Egypt will not dissuade us from the war against our nation's first enemy," a statement released by the group said.
Residents of Eilat late Monday heard two loud explosions believed to have originated from the Sinai. The rockets exploded outside city limits, Israel Radio said.
Toward midnight Monday three rockets fired by Palestinians in Gaza exploded in open areas in Israel's western Negev. No injuries were reported, Israel Radio said.
Egypt has been holding talks with Hamas in Gaza on Israel's behalf to prevent the situation from deteriorating, the report said. Recently, Hamas deployed hundreds of its members along the Gaza border fence with Israel to prevent rocket fire, the report said.