Lebanon's state-run National News Agency, however, said the Israeli soldiers shot into the air when they saw a Lebanese army patrol near the border demarcation, known as the "Blue Line".
There were no reports of casualties.
Israel said the suspects approached an area on the Israeli side of the border where its forces were carrying out an operation to shut down tunnels that were dug across the border by Hezbollah.
Israeli military spokesman Lieutenant-Colonel Jonathan Conricus told reporters that three civilian-dressed individuals identified as Hezbollah operatives tried to use the heavy fog and rain in the area "to approach and interfere with, or to take, sensors" that had been deployed there by the army.
But Lebanon gave a different account of the incident. "Israeli enemy soldiers shot into the air following their deployment near the Blue Line in Kroum al-Sharaqi region to the east of Meis al-Jabal village," NNA said.
The Israelis "were surprised, due to thick fog, by a routine Lebanese army patrol inside the Lebanese territories," it added.
Israel's military said on Tuesday it had found passages dug across the Israel-Lebanon border to be used for carrying out attacks inside Israel. It sent mechanical diggers, troops and anti-tunneling equipment there to shut them down.
The situation has so far remained calm on both sides of the border. But the Israeli operation has brought renewed attention to a frontier across which Israel and the Iranian-backed Shi'ite group Hezbollah fought a war in 2006.
The Israeli military has said its activity would, for now, stop on the Israeli side of the border. But a cabinet minister said on Friday that Israel was prepared to take action in Lebanon against cross-border tunnels if deemed necessary.
The United Nations peacekeeping Interim Force in Lebanon (UNIFIL) on Thursday confirmed the existence of a tunnel near the Blue Line, describing it as a "serious occurrence".
Asked what Israel expected UNIFIL to do, Conricus said: "To go to the locations that we have singled out and pinpointed, to locate the tunnels and then to make sure that those access points are blocked from the Lebanese side."
Israeli Prime Minister Benjamin Netanyahu briefed Russian President Vladimir Putin by phone on the tunnel crackdown, the Kremlin and Netanyahu's office said on Saturday.
(Reporting by Maayan Lubell in Jerusalem, Dahlia Nehme in Beirut; Editing by Edmund Blair and Clelia Oziel)
(This story has not been edited by Devdiscourse staff and is auto-generated from a syndicated feed.)