As NPR's Estrin reports, "All this comes hours after Israeli Prime Minister Benjamin Netanyahu met Secretary of State Mike Pompeo in Brussels and discussed Iran's involvement in the region".
Israeli army spokesperson Jonathan Conricus said the "attack tunnels" detected were not yet operational.
Cold war: The Israeli army announced the discovery of the tunnels this morning and said it has already started destroying them.
Netanyahu said he discussed the operation with Pompeo and called the tunnels a violation of a United Nations truce resolution that ended a 2006 war between Israel and the Shiite militant group Hezbollah. The tunnels are proof, he added, that bolsters Israel's long-held opinion that Hezbollah's military strategy includes using civilian infrastructure.
Israel has launched what it calls "an operation to expose and neutralise" tunnels between Lebanon and Israel allegedly made by armed group Hezbollah.
"Anyone who tries to harm the state of Israel will pay a heavy price", Netanyahu warned Hezbollah on Tuesday as the Israel Defense Forces continued its large-scale operation to destroy the terror organization's tunneling operations.
Education Minister Naftali Bennett also briefly threatened to resign and pull his party out of the coalition, toppling the government, if he were not given the defense portfolio, saying he would work to restore Israel's military strength.
The tunnel runs some 200 metres (660 feet), at a depth of 25 metres, Conricus said, and stretches some 40 metres into Israel. A small explosion scared him away and the tunnel was later blown up with a more powerful blast.
Despite the inherent risks, Israel's expectations for further escalation remain relatively low, mostly because the operation, for now, is constrained to the Israeli side and does not involve military attacks - at least not yet.
Some areas near the border fence had been closed off.
An Israeli military digger works on the Lebanese Israeli border next to a wall that was built by Israel in the southern village of Kafr Kila Lebanon
These Hezbollah special forces would, in the event of a war, bring these new abilities with them into a new conflict with Israel.
Conricus said that Hezbollah has been developing an offensive plan against Israel that would "shift the battleground into Israel".
It said the army had "enhanced its presence and readiness" and was prepared for "various scenarios".
Netanyahu has pledged to stop Iran from entrenching itself militarily in Syria and to keep it from transferring advanced weapons to its ally Hezbollah in Lebanon.
"He's half the Israeli government, practically", Kiriakou commented on what is considered to be the "one genuine democracy in the Middle East" by outgoing US Ambassador to the UN Nikki Haley.
Before his departure, Netanyahu hinted at the Israel operation.
Advancing into Israel, Hezbollah's arsenal of rockets and mortar shells would provide them with massive cover fire.
Neither side appears interested in another full-fledged confrontation like the 2006 war, but any skirmish could spark an all-out conflict.