Israel’s military has warned that Hamas militants from Gaza are still fighting inside Israel after they infiltrated southern communities and left a reported 250 people dead.

Prime Minister Benjamin Netanyahu has told Israelis they are going into a “long and difficult war”.

Hundreds of gunmen burst into southern Israel, killing soldiers and civilians, and taking into Gaza what the army said was a “significant number” of hostages.

Israel has responded with air strikes. More than 200 people were killed, according to Palestinian health officials, and Gazans received Israeli text messages overnight telling them to leave their homes and move to city centres or take refuge in shelters.

The Israeli prime minister said in an overnight message that the war had been “forced on us by a murderous attack by Hamas”, and the first stage would end in the coming hours when most of the militants on Israeli territory had been wiped out. Israel would restore security to its citizens and win, he added. The Israeli government also said it would cut off electricity, fuel and goods supplies to Gaza.

Israel’s nightmare scenario – armed Palestinian militants at large in the south of the country – began early on Saturday, the Jewish Sabbath and festival of Simchat Torah. Gunmen cut through the Gaza perimeter fence, storming into Israel on motorbikes, paragliders and by sea. The Israel Defence Forces (IDF) spokesman said the militants numbered in the high hundreds, while more than 3,000 rockets were fired across Israel that day.

“They attacked dozens of Israeli communities and IDF bases and went door to door, house to house,” said Lt Col Jonathan Conricus. “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.”

Distressing videos have emerged of Israeli civilians running for their lives from a festival in the desert, and of women being bundled into vehicles and kidnapped.

Israelis rang into news channels saying they were hiding in their homes and scared for their lives. The town of Netiv HaAsara said 15 of its residents were shot dead by Hamas militants.