Gaza militants are continuing with a rocket and mortar barrage on Israel.
Military officials say 12 rockets and mortars have landed in southern Israel early today.
No serious injuries were reported.
A new cycle of violence began Thursday with militants ambushing Israeli vehicles near the southern border with Egypt, killing eight people.
The flare-up is threatening to ignite into wider warfare. It is also complicating relations across the region.
Egypt was drawn into the violence after at least three of its security forces were killed on Thursday while Israel was pursuing militants along their shared border.
Cairo initially threatened to withdraw its ambassador to Israel. Israel apologised and Egypt relented, but it says the apology is not enough.
Senior Israeli officials met late into the night to discuss the violence, weighing whether to step up retaliatory operations against Gaza militants who triggered the latest round of hostilities on Thursday with a roadside ambush along the Israeli-Egypt border that killed eight Israelis.
Military spokesman Brigadier General Yoav Mordechai said Israel's current response to the surge in violence - airstrikes that have killed more than a dozen Palestinians, most of them militants - was not its final word.
Israel "will not hesitate" to widen its military operation if necessary, he told Israel Radio. "We will see how things develop on the ground," he said without elaborating.
Since the ambush, militants have fired around 100 rockets and mortars on southern Israel, killing an Israeli man and seriously wounding two other people yesterday. Nearly 20 rockets and mortars struck the area early today, causing no serious injuries, the military said.
Egypt has been drawn into the violence after at least three of its security forces were killed by Israeli troops pursuing militants involved in the ambush. Cairo initially threatened to withdraw its ambassador to Israel. Israel apologised and Egypt relented, but it says the apology is not enough.
In the Egyptian capital, protesters gathered outside the Israeli Embassy for a third day today, demanding the expulsion of the Israeli envoy who is now on holiday abroad.