The Israeli military said in a statement that approximately 3,000 people had taken part in what it described as riots, in five locations close to the fence.
In the statement, the Israel Defense Forces (IDF) said protesters had burned tires and flown kites -- with what the statement described as burning items attached -- over the border.
This is the fourth straight Friday that Palestinians have participated in the "March of Return" along the border fence with Israel.
They are calling for an end to Israel's blockade of the territory and say they want to highlight their right to return to lands where their families once lived, in what is now Israel.
Since the protests began, thousands of Palestinians have been injured and 39 have been killed, according to a CNN count, based on figures from the Palestinian Health Ministry.
No Israelis have been killed or injured.
Israel says Hamas is playing a leading role in the protests. Early Friday, the IDF dropped leaflets over parts of Gaza, in which it accused the militant group of exploiting the protests to pursue its own interests.
The Israeli military has accused some demonstrators of trying to cut through the fence and enter Israel, and has warned that anyone who tries to do so will be shot.
In its statement, the IDF reiterated the military's position that troops respond with riot dispersal means and fire in accordance with the rules of engagement.
Hanan Ashrawi, a member of the Palestine Liberation Organization (PLO) Executive Committee, said earlier this month that the Israeli military's responses were "unlawful violations of international law and international humanitarian law."
The UN Security Council has repeatedly failed to pass a draft statement condemning the violence.
[Ron: Ask yourself: 'What function does the UN serve'?].