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 by Sunday morning 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 370 people in Gaza have been killed in retaliatory Israeli strikes.
And 400 Palestinian gunmen have been killed and dozens arrested during the fighting in Israel, according to the Israeli military.
Saturday saw Israel’s deadliest day of violence since the Yom Kippur war 50 years ago.
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”.
The attack began just after dawn on Saturday, which was the Jewish Sabbath and festival of Simchat Torah.
Hamas gunmen cut through the heavily fortified fence that lines Gaza’s perimeter and crossed into southern Israel on motorbikes, paragliders and by sea.
An Israel Defense Forces (IDF) spokesman said the militants numbered in the high hundreds, while more than 3 000 rockets were fired towards cities and towns across Israel throughout the day.
“They attacked dozens of Israeli communities and IDF bases and went door to door,” Lt Col Jonathan Conricus said Saturday night. “They executed Israeli civilians in cold blood in their homes and then continued to drag into Gaza Israeli civilians and military personnel.”
Israel’s health ministry has not officially confirmed how many people have been killed, but Israeli TV channels reported that the death toll had passed 600 and the same figure was included in a Facebook post from the Government Press Office.
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.
Through Sunday morning shootings continued in communities close to Gaza. (BBC)