She had been working as a volunteer medic to treat wounded protesters.
United Nations envoy for the Middle East Nickolay Mladenov tweeted that Israel needed to calibrate its use of force and Hamas needed to prevent incidents at the border.
It said that "an IDF (Israel Defence Forces) vehicle was sacked upon and a suspect was identified crossing the security fence in the northern Gaza Strip and planting a grenade which exploded as he returned to the Strip".
One rocket was intercepted by Israel's Iron Dome missile defence system and the other apparently landed inside Gaza, a statement said. Earlier this week, Gaza militants fired a large barrage at Israel, which responded with heavy strikes on Gaza installations.
The Israeli military on Saturday said that it would investigate the death but said its troops worked "in accordance with standard operating procedures". It said it struck a total of 10 targets, including weapons manufacturing and storage sites. Thousands of Palestinians took part in what the Israeli military described as violent riots at five locations along the security fence, burning tires and throwing stones.
On social media, users are fervently sharing a photo of an Israeli soldier, who's reported to have shot in Razan's chest. Since then, over 110 more Palestinians have been killed, including journalists and children.
Israeli soldiers stand at the scene of attempted auto ramming attack, in Hebron in the occupied West Bank June 2, 2018.
On Friday, the protests resumed.
Today the Palestinian Medical Relief Society mourns the loss of one of our own. It says many of those killed were Hamas members and militants trying to launch attacks under cover of the protests.
Search suspended for 2 missing after deadly plane crash off Amagansett
Grieving loved ones hunkered down at the Krupinski compound in East Hampton, with private security guards turning away reporters. The search covered more than 33 hours and saturated a 646 square-mile area before it was called off, the Coast Guard said.
The draft resolution, submitted by Kuwait on May 18, condemned Israeli violence and called for the "protection of the Palestinian people" in Gaza and the West Bank.
On Friday, a U.N. Security Council resolution condemning Israel for using "excessive, disproportionate and indiscriminate force" against Palestinians failed when it was vetoed by the United States. She was the eldest of six siblings. "Now Razan became a story", said her mother, Sabreen Alnajjar, 43.
"My angel left this place, she is now in a better place". The Israeli Air Force attacked about 70 targets on the territory of the Palestinian enclave in response, first striking Hamas and Islamic Jihad Movement installations. The blockade, meant to weaken Hamas, has caused widespread economic hardship in Gaza.
On Sunday, Gaza health ministry spokesman Ashraf al-Qudra announced the death of Mohammad Hamada, 30, who was wounded on May 14.
Israeli soldiers fired two or three bullets from across the fence, according to a witness, hitting Najjar in the upper body.
Najjar was one of the first medical volunteers at the Khan Younis protest camp, and particularly relished the idea that a woman could do that work.
Ms Najar died as she ran towards the fence to reach a casualty on Friday.
"She helped all people".