A Palestinian official who spoke to Reuters on condition of anonymity said Egypt and other worldwide players were holding contacts with Israel and Gaza to restore calm.
Israel says Hamas, the Islamist group that rules Gaza, has been orchestrating the protests to distract from their governance problems and provide cover for militants' cross-border attacks.
On Saturday the Israeli military said it was conducting strikes against Hamas "in response to the terror acts instigated during the violent riots that took place along the security fence" the day before.
Earlier, the military said its jets targeted a Hamas tunnel in the southern Gaza Strip as well as other military compounds. It said six of them were intercepted by the Iron Dome aerial defence system.
Only hours after Bennett's comment and Hamas's announcement of a ceasefire, red alert sirens sounded across the Gaza border region as mortar shells and rockets were fired towards Israel again.
In statements posted on Twitter, it said it struck two Hamas tunnels, one in southern Gaza and one in the north, as well as other infrastructure across the besieged coastal territory.
The surge in violence followed mounting public criticism of Netanyahu over failure to counter a new Palestinian tactic: incendiary kites and balloons launched from Gaza that have burned crops and scrubland in southern Israel.
At least two teenagers were killed and 14 others people injured, in what's being called the biggest attack on Gaza in four years.More news: England not a top-four team despite finishing fourth - Gareth Southgate
More than 130 Palestinians have been killed during the Israel-Gaza frontier protests which have entered their fourth month and have drawn a lethal Israeli army response.
Prime Minister Benjamin Netanyahu said Israel "will intensify the strength of the attacks if necessary".
The blasts shook homes and shattered windows, and black plumes of smoke rose from the sites of the explosions. "We have no intention to harm anyone who is not a terrorist", he said.
The Gaza health ministry said 15-year-old Othman Rami Halles was killed east of Gaza City. A police spokesman said no hits had been recorded in the city.
Hours later, Israel launched air strikes in Gaza. "The activity we are engaged in now sends a message that Israel will not tolerate rockets, explosive devices, mortar bombs or (incendiary) kites", Katz said on Israel's Channel 12 TV.
More than two million Palestinians are packed into the Gaza Strip, a territory the size of the USA city of Detroit - about 360sq km - which has been described as "the world's largest open-air prison".
On Friday, thousands of Palestinians gathered near the Gaza border for their near-weekly protest.
There have been no Israeli fatalities during the so-called "Great March of Return" demonstrations.