Al Jazeera's David Chater, reporting from Gaza, described chaotic scenes after the strike.
He said there was an overwhelming feeling of bitterness and shock among the residents.
The children were aged between seven months and five years.
Residents said an Israeli shell smashed through the ceiling of the one-storey dwelling; the dead included a teenager who was walking past the house on his way to school.
"A family was sitting and have their breakfast here and now what? We come to pick up their body parts," Abu Mohamad, a neighbour said.
Omar Abdel Nabi, a farmer, said he was driving his tractor in a nearby field when at least two explosions shook the area.
"People were screaming that a tank shell landed in the next street. I carried two people covered in blood out of a house," he said.
Reports say a member of Islamic Jihad was also killed in separate fighting during the attack.
Mahmoud Abbas, the Palestinian president said "this aggressions does not serve efforts being exerted to achieve calm".
"It obstructs the peace process," he said.
The Israeli army said Palestinian fighters were operating in the area and blamed Hamas for waging war amid a civilian population, our correspondent reported.
Captain Avital Leibowitz, a spokeswoman for the Israeli military, told Al Jazeera that two Palestinian fighters had contributed to the destruction of the home.
"These militants were carrying very large explosives, which detonated and destroyed the home. It was not the result of tank fire, as they were targeted in an air raid," she said.
"We targeted the militants, and as a result, there was a very large explosion. That explosion caused the destruction of the house, and unfortunately led to the tragic deaths of those Palestinians."
Asked why the military's account contradicted witness statements and hospital records, Leibowitz said "there is no democracy in Gaza and we hear many stories. People there are not allowed to speak freely".
Palestinian fighters regularly fire rockets from Beit Hanoun into western Israel.
|Several people were injured |
in the attack [Reuters]
The Israeli military said three rockets were fired early on Monday morning at the border town of Sderot, but no damage was caused.
Hamas said one of its snipers shot an Israeli soldier in the town, and the Israeli military confirmed one of its men was "slightly wounded" by gunfire.
The military said the operation in Beit Hanoun was launched to "ensure that rocket crews, snipers and tunnel diggers are kept away from the border".
"There are several versions of this event which are being investigated," Major Avital Leibovich, an Israeli military spokeswoman said.
"The gunmen that attacked our forces did so from a populated neighbourhood, from among houses. This is another example of them using civilians as human shields for their terrorist activities," she said.
The military wings of Fatah and Islamic Jihad have threatened retaliation.
In a televised statement they said: "We assure you this crime will not pass without punishment. We assure you that the blood of our children is of high value and that our stance towards the resistance will remain the same all over the country."
Hamas has offered a six-month truce if Israel lifts its siege on the Gaza Strip, but Israel says the move is a ruse to allow them to re-arm and recruit new fighters.
"The continued Zionist massacres are new proof that the Occupation [Israel] is not interested in calm," Sami Abu Zuhri, a spokesman for Hamas, said.
"Therefore Palestinian armed wings should continue to respond to the aggression by all possible means."
Source: Al Jazeera and agencies