Israel told Lebanon's army and UN peacekeepers on Thursday to destroy a tunnel it said had been dug by the Hezbollah movement across the border into Israeli territory.
Israel's military said this week it had identified a number of passages and sent diggers and troops close to the frontier to block them.
The peacekeepers, the United Nations Interim Force in Lebanon (UNIFIL), confirmed the existence of a tunnel near the "blue line" frontier between the two countries in a statement on Thursday.
UNIFIL "visited a location" near Metulla in northern Israel, it said, 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 said its operation would stop on its side of the border, but Israeli media on Wednesday quoted an unnamed senior official saying Israel could broaden its actions into Lebanon.
Lebanon's Foreign Minister Gibran Bassil asked his country's ambassador to the UN to "present a complaint against Israel" over its actions, 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".
All parties say the situation has remained calm on both sides of the border, the Reuters news agency reported.
But the Israeli operation has focused attention on a frontier across which Israel and Hezbollah last fought a war in 2006.
The Israeli military said in a statement that it "holds the Lebanese government, the Lebanese Armed Forces and United Nations Interim Force in Lebanon responsible for all events transpiring in and emanating from Lebanon".
It added that one of its commanders had showed one of the tunnels to the head of UNIFIL, Major-General Sefano Del Col.
"We urge... that UNIFIL take action together with the Lebanese armed forces to clear the area, clear the access to the tunnels and make sure that it is not used for [hostile] purposes against Israel," said Lieutenant-Colonel Jonathan Conricus, a senior military spokesman.
UNIFIL said in its statement it was "engaged with the parties to pursue urgent follow-up action".
Israel's Prime Minister Benjamin Netanyahu said this week that Hezbollah was planning to send fighters through the tunnels to launch attacks and he expanded on his comments on Thursday.
"Hezbollah wants to insert several battalions to our territory with the aim of isolating communities, towns and kibbutzim (collective farms) to continue its reign of terror and abductions which could take place simultaneously," he told a meeting of foreign diplomats.
Netanyahu said the tunnels were big enough to be used by motorcycles, small vehicles and groups of people.