"If Hezbollah makes the serious mistake of attacking us or confronting what we are doing now it will face unimaginable blows" in retaliation, Netanyahu said during a visit to northern Israel.

"We will pursue this operation as long as the threat of Hezbollah tunnels persists," the premier, who was accompanied by the army chief of staff, said in a statement released by his office.

His warning came after the army said it had uncovered a third Hezbollah "attack tunnel" infiltrating Israel from Lebanon, which like the other two "does not pose an imminent threat".

The military, which started a search and destroy operation along the border last week, did not reveal the exact location of the third tunnel.

"Explosive devices have been placed inside the tunnel by the IDF (Israel Defence Forces)," it said in a statement.

The army announced an operation on December 4 dubbed "Northern Shield" to destroy tunnels it said were dug under the border by the Shiite militant group Hezbollah.

"The Lebanese government is held accountable for the attack tunnels dug from Lebanese territory," the military statement said.

"IDF troops will continue to operate in accordance with the approved plan to locate and expose the Hezbollah terror organisation's attack tunnels."

Israel fought a war against Iran-backed Hezbollah in 2006 that was halted by a UN-brokered truce.

Hezbollah is the only group in Lebanon not to have disarmed after the country's 1975-1990 civil war.

Netanyahu on Tuesday said that an Israeli army delegation would be visiting Moscow to brief Russian counterparts on operation "Northern Shield".

He said the delegation, would also explain "as clearly as possible that Israel has the right and the duty to fight against Iranian military presence and act against Hezbollah's bid to attack through tunnels".

The military has said the delegation would fly to Moscow on Tuesday for a day-long visit and led by the head of army operations General Aharon Haliva.

Italy's far-right Interior Minister Matteo Salvini, who arrived in Israel on Tuesday, said on Twitter that he was flying by helicopter to see for himself the tunnels built by "Islamic extremists".