This comes after a July incident where military police arrested reservists on suspicion of sexually assaulting detained a Nukhba terrorist.
Ahead of Thursday's visit, Sukkot said "the renewal of settlement in Gaza is above all a matter of righting historical injustice."
Zvi Sukkot, who participated in the Sde Teiman riots, called settler violence a marginal phenomenon compared to Palestinian terrorism in the West Bank.
The protesters arrived at the Sde Teiman base after Military Police Criminal Investigation Division soldiers, masked, arrested several reservists on suspicion of sexual abuse of a Nukhba terrorist.
MK Zvi Sukkot, who was originally barred from entering, was able to enter through a narrow opening in the fence.
The permits have become a tool for the illegal infiltration of thousands of workers into Israeli territory, according to Kan News.
When asked who would be in charge of Gaza after the war, Zvi Sukkot said, "I can tell you who would not be, not the PA, not Hamas, and not any other party that will commit terrorism."
In response to recent sanctions led by the US, Britain, and France, MK Zvi Sukkot interviews on the BBC calling the sanctions an expression of distrust in Israeli legal and enforcement systems.
Yuval Or, whose son Dror was abducted to Gaza, shouted and chased away a Religious Zionist MK who had come to offer support to the hostages' families.
Groups like Brothers in Arms and Peace Now accused Prime Minister Benjamin Netanyahu of endangering national security with the appointment.
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