Palestinian children killed on Gaza beach
They say at least 25 people were wounded in the shelling.
The Israeli military says it has halted all shelling of Gaza and has launched an inquiry into whether ground-based artillery could have been involved.
Three other people were also killed in an Israeli air strike in northern Gaza on Friday, Palestinians said.
The incidents come a day after senior Palestinian official Jamal Abu Samhadana was killed in an Israeli air strike in Rafah, the southern Gaza.
Samhadana - the founder of the Popular Resistance Committees (PRC) - was buried in Rafah on Friday, with thousands of mourners pledging to avenge his death.
Samhadana was one of Israel's most wanted men in Gaza, and his group has been blamed for a series of missile attacks on Israel.
Palestinian leader Mahmoud Abbas condemned the Israeli strikes in Gaza.
"What the Israeli occupation forces are doing in the Gaza Strip constitutes a war of extermination and bloody massacres against our people," Mr. Abbas said in a statement carried by the Palestinian official Wafa news agency.
British Foreign Secretary Margaret Beckett MP said London was "deeply concerned by reports of the deaths from Israeli shelling of civilians, including children, on a Gaza beach".
"The killing of innocent civilians is utterly unacceptable and we urge the Israelis to undertake an investigation into this incident," Ms. Beckett said.
Palestinian officials say the six people killed on the Gaza Strip beach included two women as well as the three children.
The first television pictures revealed a terrible scene, the BBC's Alan Johnston says.
At least four figures lay unconscious on the ground, possibly dead, our correspondent says. One of victims is a middle-aged woman, another is a child.
A little further away, a man was lying on a sand dune, perhaps fatally injured, while a child stood looking on in utter horror, our correspondent says.
He says that it looks very much as if this was a family enjoying their Friday afternoon off on the beach when disaster struck.