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".
The deadliest day of violence in Israel since the Yom Kippur war 50 years ago began just after dawn on Saturday, which was the Jewish Sabbath and festival of Simchat Torah.
Gunmen cut through the Gaza perimeter fence 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 in a briefing on X, formerly known as Twitter, 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. I'm talking women, children, elderly, disabled."
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.
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 there were still eight "points of engagement" where security forces were going from house to house to confirm that they were "clean of terrorism".
They included Sderot and the nearby kibbutz of Kfar Aza, where soldiers were said to be fighting to free another group of hostages.
Residents living in communities near the Gaza frontier are meanwhile being evacuated.
Concerns are also growing for the "significant number" of Israeli soldiers and civilians, including women and children, that Lt Col Conricus said were being held hostage in Gaza.
Relatives of those missing have been asked to hand their belongings to police stations so that DNA samples can be taken.
One man, Moshe Or, told Israeli media on Saturday that he had seen his brother Avinatan and his girlfriend Noa Argamani being taken by militants into Gaza in a video posted on social media.
"I saw Noa in the video scared and frightened," he said. "I can't imagine what's going through her mind at all - screaming in panic on a motorcycle, where some scumbags are holding her and they don't let her go."
Mr Netanyahu warned Hamas that Israel held it responsible for the hostages' well-being and would "settle accounts with anyone who harms one hair on their heads".
He also said the IDF would "immediately use all its strength to destroy Hamas's capabilities" and told Gazans to leave their homes and take shelter.
The IDF said it had struck 426 targets belonging to Hamas by Sunday morning, including a compound belonging to the head of the group's intelligence department.
The multi-storey Watan Tower in Gaza City, where most of the territory's internet service providers were based, was also destroyed overnight.
Palestinian health ministry officials said at least 313 people, including 20 children, had been killed in Gaza and that another 1,990 had been injured.
The OceanNewsUK's Rushdi Abu Alouf in Gaza City says the atmosphere there has changed completely from Saturday morning, when many Palestinians were celebrating on the streets. People are now staying indoors, as the territory is rocked by explosions and clouds of black smoke engulf buildings.
Palestinian health officials say civilians have been killed in the retaliatory Israeli air strikes on Gaza
Israel's security cabinet has also cut off Gaza's electricity and fuel supplies and the entry of goods.
In a separate development on Sunday, the IDF said its artillery had struck targets in southern Lebanon and carried out a drone strike on "terrorist infrastructure" in response to an attack by the militant Hezbollah movement in the disputed Shebaa Farms/Mount Dov area. No casualties were reported.
Hezbollah said it had fired rockets and shells at three Israeli positions "in solidarity with the Palestinian resistance", despite a very strong warning from Israel and the US for other parties not to engage and risk a regional war.
The Israeli foreign ministry also said that two Israeli tourists and their Egyptian guide had been shot dead by a "local" in Egypt. It was not clear if the attack was linked to the events in Israel and Gaza.
