The Israeli army said that the demonstrations on Friday at which Najjar was killed included "thousands of rioters" at five locations along the border, "burning tyres. and attempting to damage security infrastructure".
No Israelis have been killed and only a few soldiers have suffered minor injuries.
One Israeli army vehicle was sacked on, and Palestinians planted a grenade that exploded on the Israeli side of the fence, the military said. The attacker then turned around and tried to attack nearby Israeli civilians, the military said.
Her mother shows cotton wool and bandages and says, "This is my daughter's weapon, this is what she was resisting with, on what basis did the soldier kill her?"
On social media, users are fervently sharing a photo of an Israeli soldier, who's reported to have shot in Razan's chest.
On Friday, the Palestinians protested for the 10th week in a row. Over 60 Palestinians were killed that day.More news: Australia exempted from United States tariffs on steel and aluminium
The eldest of six children, Ms. Najjar did not score well enough in her high school exams to attend university, Mr. Najjar said.
She proposed the counter resolution that described Hamas as a terrorist group and condemned the indiscriminate firing of rockets by Palestinian militants in Gaza towards Israel. Israeli officials have argued that they have a right to use deadly force to stop protesters from scaling the fence that separates Gaza and Israel. "She used to come home with blood on her uniform".
The protests, dubbed the "Great March of Return" have seen thousands gather to demand the right of return to their families' lost homes or lands, now in Israel.
Israel and Palestinian armed groups in Gaza reached a de facto ceasefire this week after the most intense flare-up of hostilities since a 2014 war, both sides signalling they did not want a wider escalation.
The Gaza protests are being organized by the territory's militant Hamas leadership and are aimed at drawing attention to the decade-long Israeli-Egyptian blockade on the territory. She had been working as a volunteer medic to treat wounded protesters.
As a volunteer emergency medical worker, she said she wanted to prove that women had a role to play in the conservative Palestinian society of Gaza.
"She never cared about what people said", Sabreen said.
Palestinian accounts are lionizing al-Najjar, saying her name will never be forgotten.
"There is an alternative", she said.