If confirmed, this would be the second round of Israeli strikes in Syria since USA announced its intent to withdraw on December 19.
Lt Col Conricus said: "We have achieved the goal that we set out to achieve a month and a half ago".
It is believed the tunnels were allowing militants to sneak across the border and carry out attacks. "The latest strikes prove that we are determined to act against Iran in Syria", the premier said, according to Israeli radio Kan.
The Israeli regime launches airstrikes on the Syrian territory from time to time, aggressive moves usually viewed as attempts to prop up terrorist groups that have been suffering defeats at the hands of Syrian government forces.
After keeping a low-profile throughout most of his term, Eisenkot gave a series on interviews over the weekend focusing on his shifting the military's attention toward Iran directly, instead of just engaging its lesser proxies, Lebanon's Hezbollah and Hamas in Gaza. Damascus has also condemned the airstrikes as a violation of its sovereignty.
Citing intelligence assessments, Israel says the tunnels were prepared in secret, over a period of years, as part of a Hezbollah plan to send as many as 1,500 fighters in a shock assault on its northern communities and military bases during any future war.
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In contrast, more than one million people in the United States became permanent residents in 2017 alone. In 2016, around 10,000 were awarded to foreign nationals.
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Israel has called on the global community to impose tough sanctions on Hezbollah and act against the state within a state operation in Lebanon.
The military said its forces would stay deployed along the border area to monitor for any other possible underground activity, and said it holds the Lebanese government responsible for everything happening in its territory.
Missile fire is seen from Damascus, Syria on May 10, 2018.
UNIFIL, the United Nations peacekeeping force in Lebanon, was informed of the latest tunnel, Conricus said.
Israeli Prime Minister Benjamin Netanyahu has vowed not to let Tehran - a supporter of President Assad - entrench itself militarily in the war-torn country.