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 on 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.
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.
Near the city of Ashkelon, Israeli forces chased several Palestinian gunmen in a stolen car, killing them in a dramatic shootout on a main road.
The IDF earlier told reporters that security forces had secured 22 locations, but that there were still eight “points of engagement” where troops were going from house to house to confirm that they were “clean or terrorism”.
They included Sderot and the nearby kibbutz (community) of Kfar Aza, where soldiers were said to be fighting to free another group of hostages.
Residents who live near the Gaza frontier are also being evacuated.
Concerns are also growing for the dozens of Israeli soldiers and civilians, including women and children, who it is believed are being held hostage by Hamas in Gaza.
Relatives of those missing have been asked to hand their belongings to police stations so that DNA samples can be taken.
Noa Argamani, 25, and her boyfriend, Avinatan Or, were among hundreds of people partying at a rave in the fields next to Gaza when the attack began. A video posted on social media showed Ms Argamani screaming in panic as she was taken by militants into Gaza on a motorbike.
A friend, Amit Parpara, told the BBC that she sent him several messages as the attack unfolded.
“My first contact with Noa was around 06:30, when the (rockets) started,” he said. “She sent me her live location, asking for someone to save her and her boyfriend. She was hiding in a hole.”
“Around 08:30 was the last message that I got from her,” he added. “I tried to tell her to stay low. I tried to contact the police and the military so that they would know their location and might find them.”
“About half an hour later, I found that video… You can see clearly her terror.”
—BBC