At least 50 protesters were injured by Israeli fire, Gaza media outlets reported.
Thousands of Palestinians joined demonstrations as part of the March of Return protests that started on 30 March to demand an end to Israel's 11-year blockade on Gaza and the right of return of Palestinian refugees to their hometowns in what is now Israel.
It said four died along the frontier east of Al-Bureij in central Gaza, two east of Gaza City and one near Rafah in southern Gaza.
PLO executive Ahmad Majdalani said his organization informed the United Nations that Mladenov's actions harmed "Palestinian national security and the unity of our people".
The Israeli military said 14,000 Palestinians thronged the border fence areas Friday.
It said they planted an "explosive device" there, which blew up and "set the security fence on fire".
During one protest in July, a Gaza sniper shot and killed an Israeli soldier.
On Friday, a bomb was detonated along the fence and a number of Gazans entered into Israel, according to IDF spokesman Lt. Col. Jonathan Conricus, who tweeted "some 20 terrorists crossed through the hole created by the IED, about 5 assaulted the IDF position and were repelled".
Addressing the unrest, Israeli Defense Minister Avigdor Lieberman chose to cut Qatari fuel shipments into the Gaza Strip in response to the mass protests. He gave the order following intense clashes between Israeli soldiers and anti-occupation protesters.
One day after vowing to "reach an understanding that will bring calm to Israel", Hamas leader Ismail Haniyeh did an about-face, cheering for the continued violence on Gaza's border.
Hamas had seized control of Gaza from Western-backed Palestinian President Mahmoud Abbas in 2007 and has since fought three wars with Israel, most recently in 2014.
Israel accuses Hamas of orchestrating the weekly border riots that have taken place since March to provide cover for attacks.