Hamas Interior Minister Fathi Hammad formed the force, which is under his direct command, and the force has operated for the past few months, Haaretz reported.
A Gaza source said the force operates "day and night, 24 hours, everywhere in the Strip, particularly near the borders with Israel."
Hamas, which has supported jihad against Israel, is relying on the force to prevent organizations such as the Islamic Jihad and the Popular Resistance Committees from firing rockets into Israel.
Hamas' forming the force "seems to demonstrate that Hamas is looking to keep things quiet on the security front so it can better establish its government in the Strip," Haaretz said.
The force had arrested members of many smaller Palestinian radical groups as well as some members of the Islamic Jihad and PRC, viewed as the leading opposition groups in Gaza.
A source said the Islamic Jihad members are usually released immediately because of what Haaretz called "understandings" between Islamic Jihad and Hamas.
Soldiers from the force wear black uniforms and travel on motorcycles and in four-wheel-drive vehicles and are authorized to shoot activists who resist arrest or fire at Hamas soldiers.
Rockets or mortars that are found are confiscated and transferred to Hamas.
The force will not act if other groups fire rockets after Israel fires first, Haaretz said.