Israeli security forces are carrying out operations to rescue hostages taken by Palestinian militants from Gaza and clear areas they seized on Saturday.
The military said troops had secured 22 locations in southern Israel but were still sweeping through another eight.
The surprise attack by hundreds of gunmen from Hamas, under the cover of intense rocket fire, has reportedly killed at least 600 people in Israel.
More than 310 people in Gaza have been killed in retaliatory Israeli strikes.
Over 400 Palestinian gunmen have been killed and dozens arrested during the fighting in Israel, according to the Israeli military.
Prime Minister Benjamin Netanyahu said on Saturday night that Israel was going into a “long and difficult war”.
He also warned Hamas, which governs Gaza, that its hideouts would be reduced to “rubble”.
Hamas leader Ismail Haniyeh said it was on the “verge of a great victory”.
Israel’s health ministry has not confirmed how many people have been killed, but Israeli TV channels reported that the death toll had passed 600.
More than 2,000 others have been injured.
Overnight, Israeli security forces rescued many people who had been held hostage – almost 50 were in the dining area of one small community.
At least 10 militants who had taken over the police station in the town of Sderot were killed.
The IDF earlier told reporters that there were still eight “points of engagement” where security forces were going from house to house to confirm that they were “clean of terrorism”.
Residents living in communities near the Gaza frontier are meanwhile being evacuated.