Violence spiked again on Friday when thousands of protesters returned to the border. Palestinians also reportedly sent a nine-year-old girl through the fence, but Israeli forces were able to send her safely back.
The mass protests are perhaps Hamas' last chance to break a border blockade enforced by Israel and Egypt since 2007, without having to succumb to demands that it disarm.
An Israeli military spokesman defended the rules of engagement.
Nickolay Mladenov, the U.N.'s Mideast envoy, urged both sides to show caution on Friday.
"Demonstrations and protests must be allowed to proceed in a peaceful manner". "Civilians, particularly children, must not be intentionally put in danger or targeted in any way".
The Palestine Red Crescent Society has "also warned of a shortage of medical supplies and of personal protective equipment for their 400-person team deployed across Gaza".
The "Great March of Return" is a weeks-long planned protest in which nearly 1.3 million of Gaza's 2 million inhabitants who are refugees are demanding their right to return to their original homelands from which they were forcibly expelled when the state of Israel was created in 1948. Hundreds more were wounded by live fire last week, according to Palestinian health officials. Witnesses say he was close to the front of the protests when he was hit. More than 1,600 others were wounded. Families of those killed receive $3,000. It has also offered $500 to anyone who suffers a critical injury and $200 for a minor injury.
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Israel has pointed to violent incidents along the border as evidence of Hamas's true aims. It says the border fence was attacked with burning tires, stones and firebombs, and in one case, by a pair of gunmen.
Israel still accuses Hamas, the political party and militant group in control of Gaza, of using the protests to infiltrate Israel to commit terror attacks.
Defense Minister Avigdor Liberman said the Passover holiday "was one of the quietest and safest we have known in recent years".
The protesters lit the tires in order to blur the vision of soldiers in the region and attempt to prevent them from opening fire, according to a Gaza-based source.
The Israeli human rights group B'Tselem launched a campaign calling on Israeli soldiers not to fire at unarmed demonstrators on Friday, taking out advertisements in newspapers.
In a statement ahead of today's protests, UN Secretary General Antonio Gutteres said: "I call upon all parties on the ground to avoid confrontation and exercise maximum restraint".
The rallies are part of a six-week demonstration that will culminate on May 15, which will mark the 70th anniversary of Israel's establishment - an event Palestinians refer to as the "Nakba" or "Catastrophe".