Prime Minister Benjamin Netanyahu insisted on Sunday that Israel would do "everything necessary" to stop Hezbollah from regrouping in Lebanon and Hamas from doing the same in Gaza.
Over the past week Israel has hit multiple targets in neighbouring Lebanon, with the Israeli military saying on Saturday it had struck Hezbollah launchers and military sites.
Gaza's civil defence agency said 21 people were killed and dozens more wounded in multiple Israeli air strikes on Saturday, as Hamas and Israel again traded allegations of violating the fragile ceasefire in place since October 10.
"We are continuing to strike terrorism on several fronts," Netanyahu said as he opened a cabinet meeting.
"This weekend, the IDF (Israeli military) struck in Lebanon, and we will continue to do everything necessary to prevent Hezbollah from re-establishing its threat capability against us.
"This is also what we are doing in the Gaza Strip. Since the ceasefire, Hamas has not stopped violating it, and we are acting accordingly."
Saturday was one of the deadliest days since the US-brokered truce between Israel and Hamas came into effect, after two years of war.
The Israeli military said an "armed terrorist" had crossed the so-called yellow line -- the boundary within the Gaza Strip that Israeli forces have withdrawn behind -- and fired at Israeli soldiers.
In response, the military then "began striking terror targets in the Gaza Strip", it said.
Netanyahu claimed Sunday that Hamas had made "several attempts" to infiltrate beyond the yellow line to "try to harm our soldiers".
"We have thwarted this with great force and also retaliated and exacted a very heavy price. That includes many terrorists we eliminated," he added.
Netanyahu said it was an "absolute lie" that Israel needed outside approval before taking action.
"We decide independently of any factor, and that is how it should be. Israel is responsible for its own security," he said.
The Israeli military and the Shin Bet domestic security agency claimed that Saturday's strikes on Gaza "eliminated the head of supply and equipment in Hamas's production headquarters".
Alaa Haddadeh "operated to transfer weapons from Hamas's headquarters to battalion and field commanders", a joint statement said.
