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In a major clash that carried the risk of escalation, Palestinian militants vowed to take revenge for the deaths of civilians and Israel warned residents of communities near the Gaza border to stay within 15 seconds of their blast shelters.
The casualty toll was one of the highest in a single incident in Gaza in recent months.
Palestinians said a crowded mourning tent in the Shijaia neighbourhood was full of people paying respects to a bereaved family man when the tank shell exploded.
Ambulances, private vehicles and motorbikes rushed the wounded to hospital, eyewitnesses said. Among those killed was an 18-year-old youth.
"The occupation's targeting of civilians was a grave escalation that must not pass in silence," said Fawzi Barhoum of the Islamic movement Hamas which rules Gaza. "Resistance must be reinforced in order to block the aggression."
Israel denies targeting civilians.
The Israeli military said an anti-tank missile was fired at an army patrol along the security fence in the northern Gaza Strip. "Four soldiers were injured as a result," a statement said.
In a separate incident at another location, four people were wounded in an Israeli air strike in the town of Khan Younis.
The clash occurs at a time of renewed tension along the Israel-Gaza frontier, only some two weeks after Egyptian mediation calmed an earlier flare-up.
In an attack on Thursday, a 12-year-old Gaza boy was killed by Israeli gunfire as troops fought a gun battle with Palestinian militants. Shortly afterwards, militants blew up a tunnel packed with explosives near the border.
The Gaza Strip, a coastal territory crowded with more than 1.5 million people, many of them refugees, is controlled by Hamas Islamists who reject Israel's right to exist. It is also the base for a number of other Islamic militant groups.
One of these, called the Popular Resistance Committees, said it had fired four rockets at communities close to the border and the towns of Sderot and Netivot in southern Israel, in what it called "the revenge invoice" for the deaths in Gaza.
There was no report of casualties on the Israeli side.
In December 2008, Israel responded to repeated rocket attacks from Gaza by bombing the enclave for a week then invading with ground forces in a three-week war in which over 1,400 Palestinians were killed and 13 Israelis died.
Israel says it holds Hamas solely responsible for and violence emanating from the Gaza Strip, regardless of which group actually fires rockets or mortars.