"Hamas is strong on the ground, no one threatens their position, and the organization is unwilling to give up control of Gaza," the warning reads, among other things, Kan reports.
Several senior managers and officers within the intelligence service are the senders of the warning addressed to the military's Chief of General Staff Eyal Zamir.
Hamas, which is designated a terrorist organization, has manufactured hundreds of explosive devices and anti-tank missiles, is recruiting and training young men, smuggling drones and re-establishing the Islamist movement's underground infrastructure, such as tunnels, according to the warning.
The recommendation to Eyal Zamir is to give orders to resume the war against Hamas - in contradiction to the American stance of adhering to the ceasefire.
Hamas is estimated to control around 40 percent of Gaza's territory. Just over half of the Gaza Strip is under Israeli control within the military's established so-called "yellow line."
Israeli Prime Minister Benjamin Netanyahu in May ordered the military to expand control of the strip to 70 percent of the territory.
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