Israeli Prime Minister Naftali Bennett on Sunday said he held the Lebanese government responsible for rocket fire launched from its territory, whether Hezbollah launched the missiles or not.
Mr Bennett’s comments came days after one of the heaviest flare-ups in violence between Israel and Hezbollah in years.
He said Israel could increase its response if the rocket fire continued.
“The country of Lebanon and the army of Lebanon have to take responsibility for what happens in its back yard,” Mr Bennett told his Cabinet.
Over several days last week, militants in Lebanon launched a barrage of rockets into Israel, drawing rare Israeli air strikes in Lebanon.
On Friday, Hezbollah fired more rockets towards Israel, which responded with heavy shelling.
“It is less important to us if it’s a Palestinian organisation that fired, independent rebels," Mr Bennett said. "The state of Israel won’t accept shooting on its land."
On Saturday, Hezbollah leader Hassan Nasrallah said he would retaliate against any Israeli air strikes on Lebanon.
Mr Nasrallah said it would be wrong to assume Hezbollah would be constrained by internal divisions in Lebanon or the country’s economic crisis.
“Don’t miscalculate by saying that Hezbollah is busy with Lebanon’s problems,” Mr Nasrallah said.
He said firing the rockets was a “clear message".
Israel and Hezbollah are enemies who fought to a stalemate in a month-long war in 2006.
On Sunday, UN Secretary General Antonio Guterres called “on all parties to exercise utmost restraint”, and said it was important for all sides “to avoid action that can further heighten tensions and lead to miscalculation".
Lebanon is experiencing economic and financial crises that the World Bank describes as among the worst the world has witnessed since the mid-1800s.
Israel estimates Hezbollah has more than 130,000 rockets and missiles capable of striking anywhere in the country.
In recent years, Israel has expressed concerns that the group is trying to import or develop an arsenal of precision-guided missiles.