Israeli naval commandos have launched an early morning raid on a beach in the north of Gaza City, as the coastal enclave suffered the bloodiest day yet of the six-day Israeli assault, with 54 Palestinians reported killed.

The raid came amid continuing speculation that Israel would launch a ground offensive in Gaza, a move likely to sharply increase the number of civilian casualties. So far, 166 people have been killed including 30 children, according to Gaza's health ministry.

In the worst single incident of the conflict so far, 22 people were killed and 45 injured when two large Israeli bombs slammed into a house in the Tuffah neighbourhood of Gaza City where the city's chief of police, Tayseer Batsh, was sheltering.

Most of the injured were returning home from a mosque when they were caught by shrapnel from the blast.

Meanwhile, militants in the Islamist-ruled Gaza Strip kept up rocket salvoes deep into Israel.

On Sunday Israel appeared poised to escalate its military campaign still further, leafleting a large area of northern Gaza and sending text messages ordering residents to leave their homes by midday in advance of a large-scale bombing campaign against what it said were rocket-launching sites in Beit Lahiya and Attatra.

As the ultimatum drew near, hundreds fled Beit Lahiya, many heading to UN-run schools which were taking in refugees.

"They are sending warning messages," said Mohammad Abu Halemah, a local resident. "Once we received the message, we felt scared to stay in our homes. We want to leave."

A leaflet dropped by the Israeli military in Beit Lahiya read: "Those who fail to comply with the instructions will endanger their lives and the lives of their families. Beware."

The 2am commando raid was the first time Israeli forces have set foot in Gaza since the beginning of the current campaign.

Hours earlier, Hamas tried to hit Tel Aviv with long-range rockets in an attack it had flagged up widely in advance on social media.

According to the Israel Defence Forces the raid, which set out to destroy nearby launchers, was "accomplished" and unconfirmed reports suggested three members of Hamas had been killed in the ensuing gun battle.

Four Israelis were reported injured during the raid after apparently being spotted approaching and being engaged by waiting Palestinian fighters.

Saad al-Dawla, the night watchman of al-Mathaf hotel, said he was sleeping when the commandos came to the beach a few hundred metres away.

"At the beginning we heard shooting from the Palestinian side. I got up and looked out the window and saw that there were people shooting from the water. Almost immediately an [Israeli] helicopter came and started shooting at the water as well," he said. "Later I heard shelling from the sea and the sounded of a warship's siren. The whole thing lasted about two hours."

Another local resident, who would only give his nickname, Abu Adam, said he had been woken by the sound of fighting coming from the beach. "I was lying on the floor with my children. We could hear the sounds of shelling and gunfire and see the windows lit up by the explosions and the flares."

Earlier in the evening 22 members of the same family were killed when two bombs demolished a house belonging to Majid Batsh, a cousin of the Hamas chief of police Tayseer, with whom he was sheltering.

All that remained of the substantial building on Sunday morning were a few concrete stumps of the pillars that had supported it. A girl aged three was among those killed in the bombing.

"They were my cousins," said Mohammad al-Batsh, 20, a civil engineering student. "I was coming home from mosque when I heard a huge explosion. At first I didn't know where the sound was coming from. The air was full of dust and smoke. It felt like an earthquake.

"When I got here, I saw destruction everywhere. The bodies were so badly burned I could not recognise anyone. Thirteen of the dead came from my cousin Majid's family. He was just a driver. There are five still missing including a pregnant woman."

On Sunday, Palestinians with foreign passports began leaving Gaza through the Erez border crossing. Israel, which is cooperating in the evacuation, said 800 Palestinians living in Gaza had passports from countries including the UK, US and Australia.

Ahmed Mohana, a US citizen, said he had mixed feelings about leaving friends and family behind in the Gaza Strip. "It is very hard. It is very tough," he said. "We are leaving our family, our relatives and brothers and sisters in this horrible situation. We have to do what we have to do."

Israel has launched more than 1,300 air strikes since the offensive began, the military spokesman Lieutenant Colonel Peter Lerner said on Sunday. Palestinian militants have launched more than 800 rockets at Israel, including 130 in the past 24 hours, the Israeli military said. Several Israelis have been wounded, but there have been no fatalities.