Israeli fighter jets struck dozens of sites across the Gaza Strip early on Saturday morning.
The rocket fire aimed by Iranian-backed Palestinian Islamic Jihad terrorist organization is silent now.
Islamic Jihad's spokesman has announced an immediate halt to Gaza rocket fire on Israel. Israel said its forces were attacked with grenades and explosive devices hurled by some of the protesters, some of whom breached the border.
In response the Israeli army carried out air strikes on around 20 Hamas targets in Gaza.
Lt. Col. Jonathan Conricus, an Israeli military spokesman, said that 34 rockets had been fired at Israel throughout the night. Other targets included the entrance to a tunnel dug to infiltrate and attack Israel, and an anti-aircraft observation post, it said.
Other eyewitnesses said several people at the hospital were slightly injured from glass shards and pieces of concrete.
A four-story building in Gaza City's Daraj neighborhood belong to Hamas' General Security Services is seen on October 27, 2018, moments before it was destroyed in an Israeli airstrike.
A spokesman for the Israeli army said more than 80 sites had been targeted in the air raids.
"The resistance will not accept the equation imposed by the enemy on the basis of killing on their part and silence on our part", the group said in a statement.
The sides have fought three wars over the past decade, and Israel and Egypt have maintained a stifling blockade on the territory to weaken Hamas.
US President Donald Trump's peace envoy Jason Greenblatt condemned the rocket fire.
The Gaza protest campaign has included frequent attempts to cut through the 10-foot-high (3-meter) wire border fence to enter Israel. Another night where parents are ushering terrified children to cover. "Palestinian Islamic Jihad cement factory", the IDF said on Twitter.
Islamic Jihad, the second largest militant group in Gaza, hailed the rocket fire in a statement as a response to "Israeli aggressions", stopping short however of directly claiming responsibility for the launches.
The demonstrators were taking part in weekly Friday protests at locations along the border.
Since the protests began, 212 Gazans have been killed by Israeli troops, according to Palestinian Health Ministry figures.
The majority have died during protests, while smaller numbers have been killed by air strikes or tank fire.
Israel accuses Hamas of orchestrating the often violent demonstrations.
The fresh violence could also scupper hopes of a deal to end the months of increasing tensions.
The rocket fire prompted a series of Israeli airstrikes against targets in Gaza.
Shortly after the IDF announcement that it had struck the Hamas headquarters in Gaza, rocket sirens sounded in Israeli communities Sha'ar HaNegev and Sderot.
Egypt also upholds the siege, restricting movement in and out of Gaza on its border.
It allowed dozens of trucks of fuel paid for by Qatar into the territory, having previously blocked their entry in response to the border violence.