GAZA CITY, Gaza Strip — The four Bakr boys were young cousins, the children of Gaza fishermen who had ordered them to stay indoors — and especially away from the beach. But cooped up for nine days during Israeli bombardments, the children defied their parents and went to the seaside Wednesday afternoon, the eldest shooing away his little brother, telling him it was too dangerous.

As they clambered over a beach jetty in the late afternoon sun, a blast hit a nearby shack. One was killed instantly. The others ran. There was a second blast, and three more bodies littered the sand.

The Israel Defense Forces acknowledged later that it was responsible for the “tragic outcome” and had intended to hit Hamas extremists.

The killings reflected the conundrum for the 1.7 million Gazans trapped between Israel’s powerful military machine and the extremists of Hamas and its affiliates, who fire rockets into Israel with little regard for how the deadly response affects Gazans. Virtually imprisoned by the tight border controls of Israel and Egypt, most Gazans have nothing to do with the perennial conflict but cannot escape it.

Gaza health official Ashraf al-Kidra said the Palestinian death toll rose to 222, with 1,670 wounded. Civilians make up about three-fourths of the Palestinian deaths, according to a running count by the United Nations.

Only one Israeli has died so far in the conflict — a civilian distributing food to soldiers in southern Israel on Tuesday evening — largely because of the effectiveness of Israel’s Iron Dome air-defense system in downing incoming rockets.

Israel’s military says it does not deliberately target civilians and takes extensive precautions to avoid killing them, and it blames Hamas for operating among in populated areas. But it has acknowledged, according to Israel Radio, that about half the people in Gaza killed so far were “not involved in terrorism.”

In a report issued Wednesday, Human Rights Watch said there was a pattern of indiscriminate Israeli strikes and called on Israel to “end unlawful attacks that do not target military objectives.” Israel has hit houses, offices and farms in Gaza with F-16 airstrikes, missiles fired from Apache helicopters and shelling from gunboats.

Human Rights Watch has also condemned Hamas for deliberately targeting civilians in Israel. Hamas and allied extremists have fired more than 1,000 rockets into Israel since July 8.

Alon Ben-David, a well-sourced Israeli military-affairs analyst, said on Israeli television that the second beach blast might have been aimed at the running children, perhaps mistaken for insurgents. He added that given the military’s technologically advanced surveillance equipment, “it is a little hard for me to understand this, because the images show that the figures are children.”

At the Bakr family house on Wednesday afternoon, women wept and cursed both Israel and Hamas. Another, Nasreen al-Bakr, noted quietly that Hamas had killed 10 of her family members in factional fighting.

Bakr, 27, said that the day before, she had opposed a proposed cease-fire, wanting to hold out for “a solution” that would end Israel’s ban on fishing more than three kilometers from shore and allow the family to resume its livelihood.

“Not today,” she said, then reconsidered, adding, “Today, too,” reasoning that her nephew’s blood should not be in vain.