"Our weapon is not directed at you," it continued, adding: "We don't want to turn our rage against you ... have mercy on the soldiers you are using as fuel in the battle."
Islamic militants are believed to be behind the August 5 assault that killed the 16 soldiers in what was the worst attack on troops from inside Egypt in living memory. Gunmen stormed a security checkpoint near the border between Gaza and Israel and killed the soldiers while they were breaking their fast for the holy month of Ramadan.
The attackers then commandeered an armored vehicle and stormed across the border into Israel, where an Israeli airstrike knocked out the vehicle and killed at least six militants.
The attacks prompted the military to launch an offensive in the increasingly volatile peninsula. Most operations there however remain limited and objectives are unclear. However, for the first time since Egypt signed a peace deal with Israel, military helicopters, tanks and troops have been deployed there a move which before had not been allowed under the deal.
The attack is also believed to have triggered a drastic political and military shakeup.
Egyptian President Mohammed Morsi ordered longtime defense minister Field Marshal Hussein Tantawi, his aid Lt. Gen. Sami Anan and other members of the military council which took power after the ouster of longtime ruler Hosni Mubarak in last year's uprising into retirement. Morsi also sacked the intelligence chief and the governor of Northern Sinai.
It is not clear who issued Wednesday's statement. It is signed by "the Jihadist Salafis of Sinai" which could refer to several small Jihadist groups that are active in the area.
Large swaths of northern Sinai have plunged into lawlessness following Mubarak's ouster, and weapons smuggled from Libya have found their way into militants' hands. The weapons and the security vacuum fueled the rise of al-Qaida-inspired militant groups which have staged several low-level cross-border attacks on Israel.