"There are still 22 locations where we are engaging with terrorists that came into Israel from the sea, from the land and from the air," army spokesman Richard Hecht told journalists, adding the Hamas attack included a "robust ground invasion".

Asked by journalists how many militants had entered Israel, Hecht said "hundreds" had "invaded" the country, adding that "hundreds" were still fighting troops inside Israel.

He said there was a "severe hostage situation in Beeri and also in Ofakim", two Israeli communities in the Negev Desert, the latter 20 kilometres (more than 12 miles) from the Gaza border.

Hecht said more than 3,000 rockets had been fired from the Gaza Strip into Israel.

"There will be a severe response to this inhumane attack, it's unprecedented," he said.

Gun battles raged into the night as at least 70 people were reported killed in Israel, while Gaza authorities reported a death toll of 232 in the conflict's bloodiest escalation in years.