Hundreds of Palestinians took part in a demonstration organised by Hamas.

Israeli warplanes bombed Palestinian sites in the Gaza Strip early on Sunday in an escalation of hostilities after earlier cross-border gunfire seriously injured an Israeli soldier and wounded 41 Palestinians, including two critically.

Saturday's violence erupted after hundreds of Palestinians took part in a demonstration organised by Gaza’s Hamas rulers to draw attention to the Israeli-Egyptian blockade of the territory.

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The Israeli military said it carried out air strikes against four weapons sites and that it had reinforced its Gaza division with additional troops.

The Hamas-run Gaza health ministry said the injured included a 13-year-old boy left in a critical condition after being hit in the head.

A 13-year-old boy left in a critical condition after being hit in the head.

"Forty-one civilians were wounded with various injuries," the ministry said in a statement, with Hamas saying "thousands" of protesters had taken part.

The Israel Border Police said a 21-year-old sniper in its undercover unit was critically wounded when he was shot by a Palestinian protester.

"His condition is critical and there is a risk to his life," it said of the wounded officer.

The injuries came during a Gaza protest organised by the enclave's Islamist rulers Hamas and other factions in support of Jerusalem, where Palestinian clashes with Israeli police helped spark an 11-day Israel-Hamas conflict in May.

Hundreds of Palestinians gathered near the Strip's heavily fortified border, where some tried to scale the border fence and others threw explosives towards Israeli troops, the Israeli military said.