At least 120 Gazans were wounded and three Hamas fighters were among the four Palestinians killed in the military strikes.
Israel says Hamas has been orchestrating the demonstrations to provide cover for militants' cross-border attacks.
The Israel Defense Forces (IDF) have announced that one of their soldiers was murdered by a Palestinian sniper on July 20.
Israel's military said the strikes in Gaza were ongoing.
"The event that happened today is something that we can not tolerate and can not allow to become a routine norm, that's why we retaliated and that's why we continue to target military targets belonging to Hamas", said Lieutenant-Colonel Jonathan Conricus, an Israeli military spokesman.
Israel resumed air attacks on Gaza after last week's projectile attacks, warning that it would take whatever action necessary to stop incendiary kites and balloons being flown over the border.
Four Palestinians were shot and killed by Israeli forces during the weekly protest on Friday, according to the Palestinian Ministry of Health.
Israel has also further tightened its blockade of Gaza by restricting use of the only goods crossing, suspending oil and gas deliveries.
Since March, Palestinians have regularly protested at the fence dividing Gaza from Israel-calling for an end to Israel's blockade and to be allowed to return to the land from which they fled during the 1948 war with Israel.
The UN's special coordinator for the Middle East peace process, Nickolay Mladenov, wrote on Twitter: "Everyone in Gaza needs to step back from the brink".
Following Friday's clashes, the UN's envoy for the Israel-Palestinian conflict called on all sides to "step back from the brink" of war. Right NOW! Those who want to provoke #Palestinians and #Israelis into another war must not succeed.
Pinpointing the primary cause of Gaza's ills as Hamas' diversion of aid money from badly needed infrastructure projects to nefarious ends, such as the purchase of weapons and other terror-based enterprises, "fighting a morally bankrupt, decades-old war that has always been lost", Kushner, Greenblatt, and Friedman observe, "Life could significantly improve in short order for the Palestinian people if Hamas allowed it".
Israeli forces on Friday suffered their first fatality of the unrest when the army said "a terrorist squad shot" a soldier on the border with southern Gaza. "[Israel] will not see them until they pay the price, just like they did for Shalit", Mr.al-Hayya said.