Dozens of terrorists in military uniform emerged from a tunnel, and were successfully stopped by the military, Turgeman added.
Uncovering the tunnels is a complex and challenging task, requiring intelligence and technology, he added.
The IDF's work in destroying tunnels, both inside Gaza and cross-border tunnels, "is disturbing the enemy," which spent years digging them,Turgeman said.
Two terrorist attack cells entered Israel from northern Gaza via a smuggling tunnel on Monday morning.
They were identified by IDF lookouts, and an aircraft was dispatched to intercept them. The first cell was struck from the air, and ten of its members were killed.
The second cell fired an anti-tank missile at a military vehicle.
The Shin Bet sent an alert to the IDF hours before the attack, warning of intentions of terrorists in northern Gaza to infiltrate the country.
The Shin Bet said a serious and complex terror attack has been thwarted "due to the readiness of the IDF on the ground, following the pinpoint alert that was sent."
Police closed roads in Sha'ar Hanegev Regional Council near the Gaza border due to the security incident.
Roads closed included Route 4 and Route 34. Residents of Erez, Nir Am, Ra'im, Ein Hashlosha were instructed to stay in their houses.
Earlier in the week, 13 Hamas terrorists were killed trying to infiltrate Kibbutz Sufa. The army said it “neutralized the threat” in that incident with an air strike on the cell.
Reuters contributed to this report.