Meanwhile, Egypt's army said that since August it has killed 184 "terrorists" in North Sinai, where militants have carried out nearly daily attacks against security forces.
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Ansar Beit al-Maqdis, or the Champions of Jerusalem, said it considers Egyptian troops to be infidels because they answer to the secular-leaning military-backed government.
The group and others based in the Sinai have been blamed for a surge of attacks against the security forces since a July coup toppled the country's former Islamist president, Mohammed Morsi.
In reaction, Egypt's armed forces launched a military offensive in the Northern Sinai province in August, going after suspected militants in the region.
Speaking at a public forum Monday, the military spokesman Ahmed Mohammed Ali said so far the operations have resulted in the killing of 184 militants and the arrest of 803 others. He said about 25 percent of those killed and arrested are foreign fighters, but didn't provide further details.
The group is believed to have ties with Palestinian militants in the neighboring Gaza Strip and officials have said other foreign militants have found refuge in Sinai during the ongoing turmoil.
Ali also said during the military operations, troops have destroyed about 786 tunnels between Sinai and the Gaza Strip, which the government blames for the smuggling of militants, weapons and extremist ideas. The border crossing with Gaza has been mostly closed since 2007 by Egypt and Israel, and the territory relies on the tunnels for access to commercial goods for a large chunk. But the tunnels also serve as a smuggling route for people and contraband.
"We have achieved great successes. We have impacted the main capabilities of the terrorists," Ali told the gathering. "There is however still cells in there. We will continue to deal with them in determination, seriousness and challenge."
Ansar Beit al-Maqdis however said it "will be more determined to fight" the military and police if its warning is ignored.
"Repent from participating in the making of this infidel bastion that is at war with God and his Prophet, and stop serving in its ranks," the statement dated Sunday said.
The group gained notoriety after expanding its operations outside of the restive northern Sinai province. It has claimed responsibility for a September suicide bombing that targeted Egypt's interior minister, who escaped unharmed.
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