"Some people believe we are idiots to think the Israelis will allow us in, they may not, but we will not stop trying to return", said a protester, 37-year-old civil servant Ahmed, as he stood on a hilltop overlooking the Israeli fence.
This comes a day after an explosive device was activated on a bulldozer near the Gaza-Israel border.
Israel says it has been warning Gazans for weeks not to approach the border fence, and accuses Hamas, the armed Islamist group that controls Gaza, of instigating the protests.
Soldiers involved in the filming "would be dealt with", said Israel's defence minister Avigdor Lieberman, who claimed the sniper "deserves a medal", according to a BBC report.
Limited clashes between stone-throwing Palestinians and Israeli soldiers began in at least two places along the border, AFP reporters said, with larger protests expected after Friday Muslim prayers.
The Palestinian killed was identified as Muhammed Hujeila, 30, Palestinian medical officials said on Thursday morning.More news: Qualcomm job cuts stand at 1500 in California, more elsewhere
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The video clip which was first posted on Monday and has been widely shared on social media shows that the soldiers from Israel are heard discussing opening fire on what appeared to be Palestinians posing no immediate threat, nor engaging in any hostile acts near the fence.
Even the marches are coordinated by Gaza's Islamic militant Hamas, however, turnout is also becoming pushed by desperation among the 2 million taxpayers of the territory. The protests are part of the planned six-week "March of Return" which will end in mid-May with the anniversary of Israel's founding, which the Arab world calls the Nakba, or catastrophe.
"We will return to Palestine, our villages and Jerusalem", Haniyeh said in a fiery speech at one of five protest camps set up along the border.
The IDF expects protesters to throw Molotov cocktails and burn Israeli flags.
The International Criminal Court's prosecutor, Fatou Bensouda, warned both Israel and Hamas that each could be committing crimes - as if a terror group using violence to breach a border and a nation defending itself are equivalent.