During the incursion, a missile smashed through the ceiling of one family's one-storey house while they were having breakfast, witnesses said.
A mother and four of her children - two girls and two boys aged between one and six - were killed, doctors at a local hospital said.
"I left the house just moments before to look for one of my children. I heard the sound of the explosion, and when I returned to the house I found my wife and my children," said 70-year-old father Ahmed Abu Maateq.
"They had been eating breakfast and my wife had been holding our youngest child in her hands," he said.
"I hope to God that the same thing that happened to me happens to whoever fired that missile at my house, that what happened to my wife and children happens to his family," he said.
Several other people were injured by the blast, some of them critically.
Residents said no militants were killed by the explosion.
An Israeli military spokeswoman said the air force and army had attacked gunmen who fired upon its troops during an operation in the area launched to "ensure that rocket crews, snipers and tunnel diggers are kept away from the border fence".
Aftermath of the raid in the Gaza
The Israeli army said it had "targeted from the air two Palestinian gunmen who were approaching the soldiers while carrying large bags on their backs.
"A big explosion erupted on the scene... indicating the presence of bombs and explosives in the gunmen's bags," the army said.
"As a result of this big explosion, extensive damage was caused to a house that was near the gunmen and uninvolved civilians were hit."
Mr Abbas told the Palestinian Wafa news agency the incident "does not serve efforts being exerted to achieve calm, and it obstructs the peace process".
Hamas said one of its fighters had earlier shot an Israeli solder in Beit Hanoun. The Israeli military confirmed a soldier was slightly wounded.
More than 400 Palestinians have been killed in the Gaza Strip in the last five months, many of them civilians.
The militant group Hamas has run the Gaza Strip since June 2007, when its fighters drove out the forces of Mr Abbas's Fatah movement.
Also on Monday, the UN said it would resume deliveries of food aid to the Gaza Strip.
The UN suspended distribution of aid last week amid fuel shortages caused by cuts in Israeli supplies to the area and a strike by Palestinian petrol station owners.
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