More than 30 hours after militants from Gaza surged across the border, Israel’s military said its forces were still battling gunmen on Israeli territory. Around 600 Israelis are believed to have been killed and more than 370 Palestinians are dead.

The ongoing fighting came as Prime Minister Benjamin Netanyahu warned of a “long and difficult war” ahead, saying in a statement that Israeli forces were moving into an “offensive phase, which will continue with neither limitations nor respite until the objectives are achieved”.

A senior Israeli defence official said an early assessment suggested that about 600 Israelis were killed on Saturday. The official spoke on the condition of anonymity because the official was not authorised to speak publicly. At least 370 Palestinians have been killed, according to the Gaza health ministry.

The land, sea and air assault on Israel launched by Palestinian militants on Saturday prompted Israel to respond with heavy strikes on Gazan cities, which continued into Sunday morning. The Israeli military reported that fighting was under way in seven border communities and an army base, and tanks were seen crossing farmland in parts of southern Israel, heading south towards Gaza.

Hamas, the militant group that controls Gaza, continued to fire rockets into Israel, hitting the city of Sderot and injuring at least one person.

Scores of reservists waited at rural bus stops, trying to get to their bases after Netanyahu issued a call-up. In one potential indication that Israel might be preparing for a broader operation inside Gaza, the Israeli military said it was evacuating residents of 24 villages in areas near the border.

Hamas has taken Israeli soldiers and civilians into captivity, which could complicate any retaliatory operations. A video verified by The New York Times appears to show several Israelis being taken hostage by Hamas militants in the Be’eri kibbutz, just under 5km from the border.

As Israel’s military began releasing the names of soldiers killed in the assault, witness accounts of the battles with Palestinian militants were emerging.

“There were terrorists inside the kibbutz, inside our neighbourhood and — at some point — outside our window,” Amir Tibon recalled in a phone interview. “We could hear them talk. We could hear them run. We could hear them shooting their guns at our house, at our windows.”

The Israeli government said on Saturday evening that it was cutting off its electricity supply for Gaza, which gets two-thirds of its power from Israel. The streets of Gaza City, the enclave’s largest urban area, had emptied out amid concerns of an intensification in airstrikes.

The White House said President Joe Biden was briefed Sunday on the situation in Israel and directed “additional support for Israel in the face of this unprecedented terrorist assault by Hamas”.

Officials have not yet said what that additional assistance will be, but secretary of state Antony Blinken said the government was working to fulfil specific requests from the Israeli government for military assistance.

Egypt and Jordan, which share borders with Israel, are joining efforts to de-escalate the conflict. The two nations have relatively stable relations with both Israel and Palestine.

New York Times News Service