The UN's Office for the Co-ordination of Humanitarian Affairs (OCHA) also said it was "deeply concerned" and called for the protection of medical workers.
The Israeli army said Saturday cases such as Najjar's "in which civilians are allegedly killed" by Israeli fire "are thoroughly examined" by an internal military committee.
The Iron Dome missile defense system intercepted three of four rockets fired on Israel during the attacks.
None of Gaza's militant groups claim responsibility.
The United Nations Security Council on Friday failed to adopt two competing draft resolutions; one produced by Kuwait, in response to the killing of dozens of Palestinian protestors in Gaza, and the other tabled by the United States, which vetoed the initial resolution saying it was "grossly one-sided" against Israel. It said it struck a total of 10 targets, including weapons manufacturing and storage sites. "No IDF troops were injured".
The Israeli military confirmed in a statement it had carried out the air strikes, adding that "the Hamas terror organization is exclusively responsible for all events that transpire in the Gaza Strip and emanate from it".
Instead, Israeli military spokesman Jonathan Conricus told CNN that "quiet will most likely be met with quiet and terror will be met with a very strong response". About 1,000 Israeli settlers live in the heart of the flashpoint city, protected by the Israeli military.
The U.S. resolution deletes the reference to Israeli force and protecting Palestinians. Israel says most were attackers.
Kuwait presented its draft two weeks ago, initially calling for an worldwide protection mission for the Palestinians as protests turned violent on the Israeli-Gaza border.
A 21-year-old Palestinian well being employee was killed on Friday, the Gaza Well being Ministry stated.
Today the Palestinian Medical Relief Society mourns the loss of one of our own.
Israel withdrew its troops and settlers from Gaza in 2005, but maintains tight control of its land and sea borders, for security concerns. "She will leave a large emptiness at home". The blockade, meant to weaken Hamas, has caused widespread economic hardship in Gaza.
Razan's colleague Shaimaa said Israeli forces had started firing at the medical crew while they were discussing how to assist wounded protesters.
Razan was killed when an Israeli sniper shot her in the back, and the bullet went through her heart.
Footage circulating on social media showed Israeli soldiers pulling a man's body out of a small tractor standing in a street.