Israeli military spokesman Lt. Col. Jonathan Conricus said the military had detected tunnels crossing from Lebanon into northern Israel. He said the Israeli operation to counter the tunnels would be inside Israel, and would not cross the border.
Israel released video footage of digging and pile-driving equipment at work in unidentified locations with trees and bushes in the background, carrying out what it said were "tactical preparations to expose Hezbollah's offensive cross-border tunnel project." Reuters could not immediately verify the footage.
On Monday, Netanyahu met with U.S. Secretary of State Mike Pompeo in Brussels. An Israeli government source said the purpose of the meeting was to update Pompeo of the upcoming tunnel operation.
The current focus of operations was near the Israeli border town Metulla, Conricus said, adding that some areas near the border fence had been closed off. An Israeli military source said the operation might take weeks to complete.
The military said the tunnels were not yet operational but posed "an imminent threat" to Israeli civilians, and constituted "a flagrant and severe violation of Israeli sovereignty."
It said the army had "enhanced its presence and readiness" and was prepared for "various scenarios".
Israel and Iranian-backed Shi'ite Hezbollah last fought a war in 2006, but tensions have been rising in recent months.
During an address to the United Nations in September, Israeli Prime Minister Benjamin Netanyahu identified three locations in Lebanon where, he said, Hezbollah was converting "inaccurate projectiles" into precision-guided missiles. He warned the group that Israel would not let it "get away with it."
A few weeks ago Netanyahu also hinted at an upcoming Israeli offensive during a televised address. He offered no details, but said: "I will not say this evening when we will act and how. I have a clear plan. I know what to do and when to do it. And we will do it."
He said an upcoming security challenge would require Israelis to "endure sacrifice."
Israel's vulnerability to tunnels was laid bare during its war with Palestinian militant group Hamas in Gaza in 2014.
What began then as shelling exchanges with Hamas escalated into a ground offensive after Palestinian militants used dozens of secret passages dug from Gaza into Israel to launch surprise attacks.
Hezbollah, founded in 1982 by Iran's Revolutionary Guards, has grown stronger since the 2006 war with Israel, notably through its role in the Syrian war fighting in support of President Bashar al-Assad.
Over the past decade, Israel and Hezbollah have largely maintained a stand-off - the group has rarely launched attacks into Israel from Lebanon and Israel has rarely struck against the group on Lebanese soil.
But in the past few years Israel has struck dozens of times inside Syria at what it said were advanced weapon deliveries to Hezbollah.
(With inputs from agencies.)