"More broadly, we call on Iran and all of its agents to stop their regional aggression and provocation, which pose an unacceptable threat to Israeli and regional security", Bolton said.
The operation comes hours after Prime Minister Benjamin Netanyahu held a last- minute trip to Brussels to meet US Secretary of State Mike Pompeo.
The army went on to say that "In October 2014, a special operational engineering team was established in the Northern Command to expose and identify Hezbollah's offensive tunnels, while at the same time a project began to fortify the border, which included drilling into the ground".
"Army officials won't say how many tunnels they found, but that Hezbollah has dug them to cross into Israel and carry out attacks", NPR's Daniel Estrin reports from Jerusalem.
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The military said the tunnels were not now being used by militants and that its work to find and neutralize them was taking place inside Israeli territory.
Israel has warned that another war with the group is likely and has said it will use massive military force in any new fight.
The attack tunnels have always been rumored to have been dug from southern Lebanon into Israeli territory by the Iran backed terror group, but Israeli defense officials repeatedly either denied their existence or refused to discuss it.
IDF officials estimated the operation would last for a few weeks, but a response from Hezbollah could prolong it further.
In 2012, Israel became aware of Hezbollah's "plan to conquer the Galilee", as it was termed by Hezbollah leader Hassan Nasrallah.
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The tunnels are concentrated in the area around Metula, a small Israeli town of around 1,000 people nestled against the border with Lebanon.
However, a friendly fire incident in Syria in September that led to the downing of a Russian plane by Syrian air defences during an Israeli strike has complicated Israeli operations there.
Israel appears increasingly concerned that Iran is attempting to transfer some of its military influence from Syria, where Russian Federation is the government's top ally, to Lebanon.
Since the end of the 2006 war, Israeli forces have regularly violated Lebanon's sovereignty, with the regime's officials threatening another military offensive against the Arab country.
The UNIFIL peacekeeping force was tasked with ensuring "the immediate cessation" of attacks by Hezbollah and the cessation of all military operations on the border by both sides under UN Security Council Resolution 1701, adopted to end the 2006 war between Lebanon and Israel. In recent years, Israel has destroyed dozens of tunnels dug by Hamas under their shared border.
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Russian Federation subsequently upgraded Syrian air defences with the delivery of the advanced S-300 system, which Damascus had said last month would make Israel "think carefully" before carrying out further air raids.