Israel's lethal response has drawn global censure.
Palestinian news agency Maan identified the killed man as Rami Sabarna, 35.
"As we entered the fence to retrieve the protesters, the Israelis shot tear gas at us", the 29-year-old, who is not related to Razan, told Al Jazeera on Saturday.
"Further proof was not needed, but it is now completely clear that the U.N.is hopelessly biased against Israel", she said.
The latest escalation came hours after thousands of Palestinians attended the funeral of a young female volunteer medic killed by Israeli fire in violence on the border in southern Gaza.
Demonstrators at Friday's protests waved Kuwaiti flags to thank the Persian Gulf state for blocking a USA bid to condemn Gaza rocket fire at the Security Council earlier this week.
The United States said it would veto a U.N. draft resolution calling for the protection of Palestinians in Gaza and the West Bank.
The report did include a no comment from Israel's military spokesman, Lt. Col. Jonathan Conricus, who is normally voluble when he is inventing violence by Gazans.
The Israeli army has confirmed the attacks, claiming they were launched in response to rockets fired at the occupied territories. He has since been unemployed.
Najar, a 21-year-old volunteer medic, was shot as she ran toward the fortified border fence, east of the south Gaza city of Khan Younis, in a bid to reach a casualty, a witness said.
Najjar, 44, said his daughter rose before dawn on Friday to eat and pray before the start of the daily, sunrise-to-sunset Ramadan fast.
"I wish I could have seen her in her white wedding dress, not her shroud", she said.
"Being a medic is not only a job for a man", Razan al-Najjar, 20, said in an interview at a Gaza protest camp in May. Witnesses said she was shot in the chest. And to send a message to the world: "Without weapons, we can do anything". He said she was just 100 yards from the border fence when she was killed and he had to carry her to an ambulance.
Her father carried her blood-stained medical jacket, while other mourners demanded revenge.
"Razan was not shooting", Ibrahim said.
She arrived at a field hospital in serious condition, the hospital manager, Dr. Salah al-Rantisi, said.
After Najjar died in the operating room on Friday, Nickolay Mladenov, the United Nations.
Ambassador Nikki Haley said the United States will "unquestionably veto" the draft resolution, which Kuwait has put forward on behalf of other Arab countries, in the Security Council vote scheduled for Friday. But it concentrates on whether, as a woman, she has any difficulty doing her job as a health worker. "If they don't want to accept us by choice, they will be forced to accept us".