Reports from Gaza's health ministry said that at least seven Palestinians had been killed and almost 1,000 more injured by Israeli army gunfire.
Mounds of tyres were set alight to launch the second week of demonstrations.
At least 25 Palestinians have died since protests near the border fence began on March 30, according to the Palestinian health ministry in Gaza.
Tens of thousands of Palestinians are holding a six-week-long protest in tent encampments along the fenced border of the Israeli-blockaded Gaza Strip.
But large groups have ventured much closer to the no-go zone along the border, risking live fire from Israeli troops.
The protesters, including Palestinian refugees and their descendants, are seeking to regain homes in what is now Israel that were occupied during its 1948-1949 war.
The United Nations earlier on Friday called on both sides to refrain from violence.
"I call upon all parties on the ground to avoid confrontation and exercise maximum restraint. I particularly urge Israel to exercise extreme caution with the use of force in order to avoid casualties. Civilians must be able to exercise their right to demonstrate peacefully," said UN Secretary General António Guterres.