Conricus said the tunnel was detected less than two miles from the Israeli village of Kissufim, but that no Israelis had been in danger.
A source for the Islamic Jihad militant group said Arafat Abu Marshould, head of the group's armed wing in central Gaza, was killed with a senior associate and two other gunmen, adding that the group's fighters were on "full alert".
"This is a severe violation of Israeli sovereignty and must not be overlooked", an IDF spokesman said.
Prime Minister Benjamin Netanyahu said Israel had used "breakthrough technology" to find and destroy the tunnel.
Meanwhile, Fatah, the West Bank-based political party of Palestinian President Mahmoud Abbas, called for dialogue between Palestinians to discuss the best response to the Israeli bombardment.
Defense Minister Avigdor Liberman took the offensive, charging Bennett with making irresponsible comments.
Iran's Foreign Ministry on Monday strongly condemned the recent Israeli airstrike on the Gaza Strip, describing the attack as "brutal". An IDF spokesperson said while the underground passage extended under Israeli territory, there was no tunnel opening on the Israeli side, according to the Ynet news website.
Hamas decried the attack as the "latest Zionist crime".
Iran "supports the resistance in Palestine as well", al-Arouri said, in remarks translated by the Middle East Media Research Institute (MEMRI).
The discovery of the attack tunnel-whether constructed with Hamas' tacit approval to achieve plausible deniability or at its explicit directive-creates additional problems when viewed against the backdrop of the unity deal signed with Abbas' Fatah faction.
The Islamic regime in Gaza will likely continue to remain the real power in Gaza and will continue investing in its vast subterranean terror infrastructure. "Tehran has attempted to do this through Islamic Jihad, which it created and completely controls, and also by financing Hamas". "The Agency again demands full respect for the neutrality and inviolability of United Nations premises at all times". With only three hours of electricity available per day, the U.N. warned that half of Gaza's population is in need of immediate humanitarian aid. Hamas leaders recently concluded a unity agreement with the Palestinian Authority.