After two days of rocket strikes, the Israeli army Monday said it has regained control of southern areas near the Gaza Strip which was taken over by Hamas on Saturday.

"We are in control of the communities," military spokesman Daniel Hagari told the media.

However, he cautioned that individual Hamas troops may remain in the region.

Israel's military said that it eliminated gunmen who infiltrated from Lebanon.

Over the last three days, the toll has surpassed 1300 with Israel alone counting more than 800 dead. Palestinian officials claimed that Israel's barrage of air strikes on Gaza has taken the toll there to 560. The US has confirmed that nine of its citizens have died in the strikes.

Meanwhile, more than 1,23,000 Palestinians have been forced to flee their homes in the Gaza Strip.

Defence Minister Yoav Gallant said Israel would impose a "complete siege" on the long-blockaded enclave. It will impact 2.3 million people who will be left with no electricity, no food, no water, and no gas.

Palestinians in the impoverished and crowded coastal territory are bracing for an Israeli ground attack aiming to defeat Hamas and liberate at least 100 hostages.

On Day 3 of the war, skies over Gaza were seen blackened by thick plumes of smoke as fighter jets roared above. Hamas kept firing rockets as far as Jerusalem, where air raid sirens blared and detonations were heard.

"Overnight IDF fighter jets, helicopters, aircraft and artillery struck over 500 Hamas and Islamic Jihad terrorist targets in the Gaza Strip," a statement by the Israeli Defense Forces said.

Israel Prime Minister Benjamin Netanyahu has warned Gaza civilians to get away from all Hamas sites which he has vowed to turn "to rubble".

Israel was hit by an unprecedented rocket attack from the Gaza Strip on Saturday morning.

The Israeli army said Hamas fired more than 3,000 rockets, adding that dozens of Hamas troops infiltrated border areas in southern Israel.

The Israeli military has since sent troops to the southern territories to reconquer them from the Palestinian forces and has started conducting strikes at Hamas' positions in Gaza.

The Israeli government announced on Sunday that it had invoked Article 40 of the Basic Law, which means the country officially entered a state of war.

Both sides report hundreds of dead and thousands of injured as a result of the escalation of the conflict.