Three Palestinians were killed on Sunday as they attempted to cross the border and damage security infrastructure, Israel's Defense Forces (IDF) reported.
The Israeli military said four men arrived in the area of the fence "with the intention of infiltrating and conducting a terror attack".
Gaza's health ministry confirmed the deaths, identifying the casualties as Abdel Rahman Qudeih, 23, and Mohammed Abu Rayda, 20.
Gaza's health ministry confirmed six people were killed, updating the figure from an initial five, and three others wounded in what residents said appeared to be an accidental explosion in the Az Zawayda area of the central Gaza Strip.
It came a day after Palestinians staged a sixth weekly mass protest on the border.
The protest campaign is scheduled to run until May 15, when organizers expect a million people to turn out to mark the 70th anniversary of the founding of Israel, which Palestinians call the "nakba" or "catastrophe".
No Israelis have been hurt in the weeks of protests and occupation forces have faced global criticism for their use of live ammunition.
Israeli media have in recent days alleged damage to farms due to kite-flown Molotov cocktails, though the devices face hard odds in making it across the fence while staying alight.
Security officials have warned protesters that approaching the border fence puts their lives in jeopardy.
Palestinians sent several stunt kites with incendiary bombs over the border towards Israel Friday.
Since the "Great March of Return" began, some 7,000 Gazans have been injured and 45 killed, according to the Palestinian News agency Wafa.
It accuses Hamas of seeking to use the protests as cover to carry out violence.
The statement was unclear about whether the Palestinians managed to get into Israel. Two of the terrorists were killed, said the IDF.
Israel says Hamas, the militant group which dominates Gaza, is orchestrating the demonstrations in order to launch attacks.
- One person shot in 'dispute' at Nashville's Opry Mills Mall
- Lightning nix Bruins with win in Game 5
- MI keep breathing; beat KXIP by 6 wickets
- Manchester United coach in intensive care after surgery
- Day gets wet, but leads Wells Fargo by two strokes
- WhatsApp iOS version now enabled to play Instagram and Facebook videos
- Rebels, Indian troops clash in Kashmir's main city; 1 killed
- Nobel Prize In Literature For 2018 Cancelled Over Sexual Misconduct Scandal
- Royal Wedding Guide: Who is going to be in the wedding party?
- Talent Not an Issue for England's New Manager