Razan al-Najjar, 21, a volunteer with the Gaza health ministry, was fatally shot in the chest near Khan Yunis on Friday.
Ambulances and medical crews attended the funeral, with her father holding the white blood-stained medics' jacket she wore when she was shot, as mourners called for revenge.
Gazans have since March 30 staged border protests demanding the return of Palestinians to land they fled or were expelled from during the 1948 war surrounding Israel's creation, now inside the Jewish state.
Israeli army kills 21-year-old Palestinian nurse in Gaza border protest
The demonstrations are accompanied by smaller clashes as youths hurl stones at Israeli soldiers and attempt to breach the border fence, at times laying explosive devices on the fence or throwing grenades.
Palestinians in the besieged coastal enclave have also been using kites carrying cans on fire to set ablaze Israeli fields, torching extensive patches of agricultural land near Gaza.
Following the funeral, several Gazans were wounded in clashes east of Khan Yunis, health ministry spokesperson Ashraf al-Qudra said.
The Israeli army said "a terror cell" had infiltrated from southern Gaza. Soldiers shot at the Palestinians, who returned to the enclave.
On the Friday clashes, the army said it had included "thousands of rioters" at five locations along the border, "burning tires adjacent to the security fence and attempting to damage security infrastructure".
Shots were fired at an army vehicle and a Palestinian had crossed into Israel, planted a grenade and returned to Gaza, it said.
The army said that cases such as Najjar's "in which civilians are allegedly killed" by Israeli fire "are thoroughly examined" by an internal military committee.
S vetoes UN resolution denouncing violence against Palestinians
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."
The Palestinian Medical Relief Society said Najjar was shot "as she was attempting to provide first aid to an injured protester", with three other first responders also hit by live fire on Friday.
"Shooting at medical personnel is a war crime under the Geneva conventions," the PMRC said in a statement, demanding "an immediate international response to Israeli humanitarian law violations in Gaza".
Najjar's death brings the toll of Gazans killed by Israeli fire since the end of March to 123.
The demonstrations and clashes peaked on May 14 when at least 61 Palestinians were killed in clashes as tens of thousands of Gazans protested the US transfer of its embassy in Israel to the disputed city of Jerusalem the same day.
Low-level demonstrations have continued since.
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".
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ