The army earlier detected the subterranean construction activity with new technological means and chose an opportune time to destroy it, Israeli military spokesman Lt. Col. Jonathan Conricus said.
According to the latest from Gaza's health ministry, five members of the terrorist group were killed in the explosion and nine more were injured.
Abu Eita said that despite the incident, the Palestinians would push ahead with the unity plan. "The implementation of the reconciliation agreement is the optimal response to this crime", he said.
Israel deployed its Iron Dome anti-missile system in the area and declared the border region a closed military zone. Conricus said the Israeli military was not seeking further escalation.
Prime Minister Benjamin Netanyahu said Israel had used "breakthrough technology" to find and destroy the tunnel.
Israeli soldiers patrol close to the Israeli border with the Gaza Strip on October 30, 2017, near Kibbutz Kissufim in southern Israel. The tunnel extended for over a mile, some of it deep into Israeli territory.
The incident comes only days before Hamas is expected to hand over control of Gaza's borders to the internationally recognized Ramallah-based Palestinian Authority (PA).
Asked by reporters if Hamas, rather than another armed faction, had dug it, Conricus said: "I can not confirm that".
Israel and the United States have meanwhile said that Hamas must disarm as part of any unity government. The Palestinians also demanded to put a halt to Jewish visits to the Temple Mount, which they called "incursions by Jewish extremists into the Al-Aqsa Mosque and all the holy sites", claiming the visits create a climate of tension and push the region towards religious conflict.
The Abbas-led Palestine Liberation Organisation has recognized Israel, but Hamas has not.
Any reconciliation could actually have a detrimental effect on Middle East peace; Israel has consistently refused to negotiate with any group that includes Hamas.