One Israeli army vehicle was sacked on, and Palestinians planted a grenade that exploded on the Israeli side of the fence, the military said.
The IDF said that Israeli jets struck "five terror targets in a military compound belonging to the naval force of the terror group Hamas in the northern Gaza Strip" in response to the firing of four projectiles from Gaza.
"These terror activities included planting a grenade, hurling explosive devices, attempts to cross the security fence, damaging security infrastructure, and igniting fires in Israeli territory with the use of arson kites and balloons".
It calls for urgent steps "to ensure an immediate, durable and fully respected ceasefire" and asks UN Secretary-General Antonio Guterres for a written report within 60 days detailing recommendations about "an global protection mechanism".
Ambulances and medical crews attended the funeral, with Najjar's father holding the white blood-stained medics' jacket she wore when she was shot, as mourners called for revenge.
She was the second woman among more than 115 Palestinians who have been killed by Israeli army fire since Gaza border protests began in late March.
They came to retrieve her body from the hospital where she and her friends had cared for the injured of this increasingly bloody confrontation along the border between Israel and Gaza.
Palestinians on Friday gathered along the Gaza-Israel security fence - for the 10th consecutive Friday - to take part in ongoing rallies against Israel's decades-long occupation. The International Committee of the Red Cross (ICRC) said the number of wounded was greater than during the August 2014 conflict.
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. "She was the first female paramedic in the field", Sabreen Najar said.
None of Gaza's militant groups claim responsibility.
Following the funeral, several Gazans were wounded in clashes east of Khan Younis, health ministry spokesman Ashraf al-Qudra said.
Dozens of rockets have been launched from Gaza into Israel this week and Israeli Defense Forces have fired on demonstrators with live ammunition, killing about 60 people on May 14 alone, the day that the United States transferred its embassy from Tel Aviv to Jerusalem, UN officials said.
Low-level demonstrations have continued since.
On social media, users are fervently sharing a photo of an Israeli soldier, who's reported to have shot in Razan's chest.