"We are working on restoring peace and stability in the southern communes. But we are fully ready for a possible escalation and a broader campaign and are making preparations", Kochavi said.
The Israeli military exchanged fire with Palestinian militants in the Gaza Strip on Saturday night.
Dozens of rockets were launched from the exclave at Israel in the past two days, prompting Israel to strike back. This is the worst cross-border fighting in months.
The attacks come amid violent clashes that rocked central Jerusalem and the West Bank since the beginning of Ramadan amid complaints that the police tried to bar worshipers from Ramadan evening gatherings outside Damascus Gate.