United Nations Interim Force in Lebanon (UNIFIL) vehicles patrol along the border with Israel on December 6, 2018. (Photo: AFP)

A UN peacekeeping force Thursday confirmed the presence of a tunnel in northern Israel near the Lebanese border, after the Jewish state accused Hezbollah of digging under the frontier.

UNIFIL "visited a location" near Metula in northern Israel, it said in a statement, and "can confirm the existence of a tunnel at the location".

"UNIFIL is now engaged with the parties to pursue urgent follow-up action," it said.

"It is very important to determine the full picture of this serious occurrence."

Israel launched an operation dubbed "Northern Shield" on Tuesday to destroy tunnels it said were dug across the border by the Shiite militant group Hezbollah.

As operations continued on Thursday, the Israeli army said it had contacted UNIFIL, which monitors the border region, regarding a tunnel originating on the Lebanese side of the border.

Yoel Strik, head of the army's northern command, demanded the UN force "take action, investigate and make sure to neutralise the shaft of that attack tunnel".

Lebanon's Foreign Minister Gibran Bassil asked his country's ambassador to the United Nations to "present a complaint against Israel", his ministry said in a statement.

He accused Israel of carrying out a "diplomatic and political campaign against Lebanon, preparing to launch aggressions against it", he said.

On the Lebanese side of the border, residents in the town of Kafr Kila received a recorded voice message on their mobile phones in Arabic from Israel, the national news agency said.

The message called on recipients to distance themselves Hezbollah, NNA said.

"Your town will be exposed to danger because of the presence of tunnels linked to (Hezbollah) near your homes," the message reportedly said.

It warned residents against cooperating with the militant group.

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

It earned its moniker "the Resistance" through fighting Israel, which occupied southern Lebanon until 2000.