Tel Aviv: Over 400 terrorists have been killed inside Gaza, and dozens more have been held captive, the spokesperson for the Israel Defence Forces (IDF) said on Sunday.

At a press conference on Sunday, top IDF spokesman Daniel Hagari said the searches for Hamas terrorists were underway at several besieged towns.

"As of this hour, there are forces fighting in [Kibbutz] Kfar Aza, there are searches in a large number of towns. There are IDF forces in all towns, there is no town that does not have an IDF force in it," Israel Defense Forces' top spokesman, Rear Adm. Daniel Hagari was quoted as saying by The Times of Israel.

According to Hagari, the IDF's mission objectives are to evacuate all civilians from border communities in Gaza, put an end to fighting there, manage security barrier breaches, and keep attacking terrorist targets in the Strip.

More than 24 hours after Hamas launched rocket attacks followed by an unprecedented ground assault, firefights between forces and terrorists were ongoing in Kfar Aza, close to the Gaza border. The IDF was attempting to neutralise all terrorists still present, The Times of Israel reported.

In a major escalation on Saturday, Hamas launched a "surprise attack" on Israel, firing a barrage of rockets into the southern and central parts of the country.

The toll from the rocket attacks and ground assault by Hamas went past 300 on Sunday, with another 1,864 people reported to be injured.

Several Israelis were taken as hostages in Gaza, the Times of Israel reported citing officials.

Israeli Prime Minister Benjamin Netanyahu issued a stern warning to Hamas, claiming that it had begun a terrible war and that the Israel Defence Forces (IDF) would use all of its strength to undermine their capacity.

"Hamas forces invaded Israeli territory this morning, on the morning of a holiday and Shabbat, and murdered innocent civilians, children and the elderly. Hamas started a cruel and evil war. We will win this war, but the price is too heavy to bear. This is a very difficult day for all of us," the Israeli PM posted on 'X' on Sunday.

Netanyahu added, "Hamas wants to murder us all. It is an enemy who murders children and mothers in their homes, in their beds. An enemy who kidnaps the elderly, children, and girls. Murderers who slap and slaughter our citizens, our children, who all in all went out to spend the holiday."

He said after what happened in Israel on Saturday, he will make sure that it does not happen again.

Earlier on Sunday, the IDF said Israeli fighter jets hit a military facility at the residence of the terrorist group Hamas' intelligence chief in Gaza.

Sharing an update on the ongoing counter-offensive on social media platform X, the IDF posted a video and wrote, "Fighter jets recently attacked a military infrastructure at the home of the head of the intelligence department of the terrorist organization Hamas."

"At this time, the IDF continues its attacks throughout the Gaza Strip," the IDF added in its post.

The attack, which began at 6.30 am local time (03:30 GMT) on Saturday involved Hamas fighters, who infiltrated Israel by land, sea, and air.

Israel's military launched a series of air raids on Gaza in response to the attacks.

Senior Hamas military leader Mohammed Deif declared earlier that the attacks were the beginning of "Operation Al-Aqsa Flood", urging Palestinians all over the world to resist Israeli occupation.

Hamas would pay a "heavy price for its actions", the Israeli military told citizens living near the Gaza Strip, ordering them to remain inside their houses.

Significantly, Al-Qassam Brigades, the military arm of Hamas, referred to Saturday's attack on Israel as an effort "in defence of the Al-Aqsa Mosque", a disputed religious site significant to both Muslims and Jews.