Israeli army denies deliberately targeting Gaza nurse
Her killing sparked international outrage.
At least 125 Palestinians have been killed by Israeli snipers since unarmed demonstrations began on 30 March demanding the return of Palestinians to land they fled or were expelled from during the 1948 war surrounding Israel's creation.
No Israelis have been killed.
Following Najjar's death, the UN envoy for the Middle East, Nickolay Mladenov, said in a tweet that "Medical workers are #NotATarget!" and that "Israel needs to calibrate its use of force and Hamas need to prevent incidents at the fence."
On Tuesday there was relatively muted protest with about 100 demonstrators gathering in the northern Gaza Strip near the Erez border crossing into Israel, AFP correspondents said.
There were minor clashes in Khan Yunis and central Gaza involving dozens of protesters.
In Bureij in central Gaza, young men attached flaming plastic containers to kites hoping to set crops alight on the other side of the frontier.
The protests had been called Tuesday to coincide with the 51st anniversary of the 1967 Six-Day War when Israel seized the West Bank and Gaza.
Organisers said larger numbers were now expected Friday, which coincides with Israel's 1967 capture of Palestinian East Jerusalem.
East Jerusalem is recognised as occupied Palestinian territory under international law.