During the weekend, fires erupted at 20 sites on the Israeli side of the border.
Amid worldwide condemnation of its use of lethal force, Israel said numerous dead were militants and that the Israeli army was repelling attacks on the border fence between Israel and Gaza.
Prime Minister Benjamin Netanyahu said after the strikes that Israel's military had delivered the "harshest blow" in years to Gaza militants.
This was the scene that Najjar dashed into in her white coat to tend to an elderly man who had been hit in the head by a tear-gas canister, according to a witness, Ibrahim al-Najjar, 30, a relative of Najjar's.More news: All signs point to 'Fortnite' releasing for the Nintendo Switch
Hamas said it reached a cease-fire through mediators, while Israel said it would halt its strikes as long as there was no rocket fire.
Razan's colleague Shaimaa said Israeli forces had started firing at the medical crew while they were discussing how to assist wounded protesters.
No casualties were reported.
Thousands of people attended al-Najar's funeral in Gaza on Saturday, including some she had treated when they were wounded at previous border protests.
The United States vetoed on Friday a Kuwait-drafted UN Security Council resolution that condemned Israel's use of force against Palestinian civilians, criticizing it as a "grossly one-sided view" that failed to blame Hamas for the recent violence.More news: Gunman kills 3, including 2 police officers, in Belgium shooting
The attacks come less than a week after Egypt brokered a ceasefire between Israel and Palestinian militants following a month of unrest arising from the Great March of Return protests and the U.S. decision to move its embassy to Jerusalem. No clashes occurred and al-Najjar was on Gaza soil wearing clothing marking her as a paramedic.
"After Najjar died in the operating room on Friday, Nickolay Mladenov, the U.N. Middle East envoy, tweeted that "#Israel needs to calibrate its use of force and Hamas need to prevent incidents at the fence.
The Israeli military stated in a press release on Sunday that the Hamas movement is responsible for all acts of aggression that originated from Gaza, which is controlled by it.
Speaking at Najjar's funeral, Khaled al-Batsh, one of the protest organisers, called on Gazans to "continue the return marches and break the (Israeli) siege with peaceful tools".
Most of those killed during the protests have been shot by Israeli snipers, half of them in a single day, May 14, the peak of the campaign.More news: Syria's Assad threatens force against US-backed Kurds