At least 560 Palestinians have been killed and 2,900 wounded in Israeli air strikes on the blockaded enclave since Saturday, said Gaza's health ministry.
Meanwhile, Israel said on Monday its troops backed by helicopters had killed a number of armed infiltrators entering the country from Lebanon, raising fears fighting could spread two days after Hamas gunmen burst in from Gaza on a deadly rampage.
The Israeli military said it had called up an unprecedented 300,000 reservists and was imposing a total blockade of the Gaza Strip, signs it could be planning a ground assault there to defeat Hamas.
Hamas fighters were still holed up in several locations inside Israel two days after they burst across from Gaza killing 700 Israelis and seizing dozens of hostages in a raid that shattered Israel's reputation of invincibility.
Prime minister Benjamin Netanyahu told mayors of southern towns hit by the surprise assault that Israel's response would "change the Middle East".
In Hamas-controlled Gaza, Israel pressed on with its most intensive retaliatory strikes ever, which have killed more than 500 people since Saturday.
Defence minister Yoav Gallant announced Israel's tightened blockade which would keep even food and fuel from reaching the strip, home to 2.3 million people.
The prospect that fighting could spread to other areas has alarmed the region. Israeli troops "killed a number of armed suspects that infiltrated into Israeli territory from Lebanese territory," the military said, adding helicopters "are currently striking in the area".
An official with Hezbollah denied that the group had mounted any operation into Israel. Hezbollah, a Shi'ite militant group powerful in southern Lebanon, is backed by Iran like Hamas.
Artillery shelling and gunfire were heard at Lebanon's southern border with Israel, a correspondent for Hezbollah's Al-Manar TV said in a post on social media. Israel's Army Radio gave the location as being near Adamit, across from the Lebanese border towns of Aalma El Chaeb and Zahajra.
In Israel's south, scene of the deadly Hamas attack, Israel's chief military spokesman said troops had re-established control of communities inside Israel that had been overrun, but that isolated clashes continued as some gunmen remained active.
"We are now carrying out searches in all of the communities and clearing the area," chief military spokesperson Rear-Admiral Daniel Hagari said. Earlier, another spokesman, Lieutenant Colonel Richard Hecht, acknowledged that it was "taking more time than we expected to get things back into a defensive, security posture".
The shocking images of the bodies of hundreds of Israeli civilians sprawled across the streets of towns, gunned down at an outdoor dance party and abducted from their homes were like nothing seen before in the decades-old Israeli-Palestinian conflict.
"We have never drafted so many reservists on such a scale," Hagari said. "We are going on the offensive."
Palestinians reported receiving calls and mobile phone audio messages from Israeli security officers telling them to leave areas mainly in the northern and eastern territories of Gaza, and warning that the army would operate there.
Hamas, an armed Islamist group that calls for Israel's destruction, says its attack was justified by the plight of Gaza under a 16-year blockade and the deadliest Israeli crackdown for years in the occupied West Bank
Mainstream Palestinian groups who deplored the attacks said the violence was nonetheless predictable, with a peace process frozen for nearly a decade and far-right Israeli leaders talking of annexing Palestinian land once and for all.
Israel and Western countries said nothing justified the intentional mass killing of civilians.
The attackersgunned down scores of young Israelis at an outdoor desert dance party - media reported 260 killed there. A day later dozens of survivors were still emerging from hiding. The site was littered with wrecked and abandoned cars.
"It was just a massacre, a total massacre," said Arik Nani, who had been celebrating his 26th birthday and escaped by hiding for hours in a field.
In Gaza, footage obtained by Reuters showed dozens of people climbing over collapsed buildings in search of survivors, the air still dusty from impact. Sirens rang out as emergency teams put out cars that had caught fire.
"The man you see is one martyr of dozens. This place is packed with residents and people who were displaced," a man said in the video as people pulled a body from the rubble.
"The Zionist enemy's military targeting and bombing of homes inhabited by women and children, mosques and schools in Gaza amount to war crimes and terrorism," Hamas official Izzat Reshiq said in a statement.
Egypt, which has mediated between Israel and Hamas at times of conflict in the past, was in close contact with the two sides, trying to prevent further escalation, according to Egyptian security sources.
Qatari mediators have held urgent calls with Hamas officials to try to negotiate freedom for Israeli women and children seized by the militant group and held in Gaza, in exchange for the release of 36 Palestinian women and children from Israel's prisons, a source told Reuters.
The violence jeopardises U.S.-backed moves towards normalising relations between Israel and Saudi Arabia - a security realignment that could have threatened Palestinian hopes of self-determination and hemmed in Hamas's backer Iran.
"The price the Gaza Strip will pay will be a very heavy one that will change reality for generations," Defence Minister Gallant said in Ofakim, one of the towns that had been attacked.
Israel's military faces harsh questions for the country's worst intelligence failure in 50 years. Netanyahu's options may also be curtailed by concern over the fate of Israeli hostages.
A ground assault would be a major step for Israel, which has sent troops back into Gaza twice since it abandoned the territory nearly two decades ago, but has tried to avoid reimposing any long-term occupation there.
Israeli officials have not confirmed any plans for a ground assault but have discussed what it might entail. Agriculture Minister Avi Dichter, a member of Netanyahu's security cabinet, likened a possible operation to a 2002 sweep of the West Bank in which Palestinian cities were encircled and then-Palestinian leader Yasser Arafat besieged in his headquarters.
"Israel cannot agree to a situation in which military terrorist organizations will exist at a proximity of a few hundred meters, a kilometre, and so all of these capabilities will be destroyed,” he told Israel's Channel 12 TV late on Sunday.
