Live updates: Israel taking 'significant military steps' in response to Hamas attack

Israel's defence minister has ordered a "complete siege" on the Gaza Strip following an unprecedented incursion into Israel by Hamas fighters.

Israel formally declared war on Sunday and gave the green light for "significant military steps" to retaliate against Hamas for Saturday's surprise attack. More than 1,100 people have been killed and thousands wounded on both sides.

The defence minister's announcement on Monday came as Israel's military scoured the country's south for Hamas fighters and guarded breaches in its border fence with tanks while pounding Gaza from the air.

A spokesperson said the Israeli military regained control of border communities taken by Hamas fighters during the attack. But Palestinian militants continued firing barrages of rockets, setting off air raid sirens in Jerusalem and Tel Aviv.

Egypt has engaged in negotiations with Israel and Palestinian militant groups to release Palestinian women in Israel's prisons in exchange for Israeli women captured by Hamas militants, the state-owned Egyptian newspaper Al-Ahram reported Monday.

The daily paper quoted an unnamed source as saying that the negotiations were aimed at finalizing an agreement on the trade.

"The Egyptian government is presently awaiting responses from both parties regarding the proposed prisoners exchange and a temporary cease-fire," Al-Ahram said.

Palestinian militant groups have claimed to be holding over 130 people who were captured in Israel in the past two days. Hamas spokesman Abdel-Latif al-Qanoua told The Associated Press by phone that the group's fighters had captured more Israelis as recently as Monday morning.

He said the group aims to free all Palestinian prisoners held by Israel, which in the past has agreed to lopsided exchanges.

Lebanese caretaker Prime Minister Najib Mikati said Monday that the tiny country's priority is to maintain stability along its southern border with Israel following an exchange of attacks between Israeli troops and Hezbollah militants over the weekend.

Hezbollah claimed responsibility for firing rockets at three Israeli positions in disputed territory along the border of the Israeli-occupied Syrian Golan Heights, before Israel