The Israeli media reported that the Israeli defense system Iron Dome intercepted Gaza militants' rockets, with no injuries reported. As a precaution, the military shut down a popular beach in southern Israel and placed limitations on gatherings of large crowds.
Saturday's exchange of missiles and rockets is considered as the biggest since the 2014 Israeli war on the impoverished sliver.
In a relatively rare admission, Hamas said it fired the rockets to deter Israel from further action.
An Israeli aircraft fired at what it said was militants launching balloons carrying firebombs over the Gaza border fence. 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.
Announcing their deaths in the strike on a Hamas facility on Saturday, the Palestinian health ministry said they were walking on a road nearby when they were hit with shrapnel from the huge blast.
The Hamas training facility in Gaza that the IAF attacked on Saturday was meant to be the "Palestinian national library", the IDF said Sunday morning.
Dawood Shihab, the Islamic Jihad spokesman in Gaza, said in a press statement that "resistance will not hesitate to respond to any Israeli aggression against Gaza, bombing will be met by bombing and blood for blood and time that attacked us without a response is ending".
Later, witnesses reported that Israeli warplanes dropped four bombs on an unfinished building near a Hamas police and security compound in Gaza City, reducing the old structure to rubble.
The bombing exposed a tunnel under the building, which the army said was "part of a tunnel network dug by the Hamas terror organization all through the Gaza Strip". It accuses Hamas of seeking to use the protests as cover for attacks against Israel.
Hamas spokesman Fawzi Barhoum said the Palestinian resistance movement had agreed to an "Egyptian offer to return to a ceasefire to stop this escalation".
Fifteen people have been wounded across Gaza, the ministry said. Hamas said another Palestinian had died after being shot by Israeli troops during border protests on Friday.
Since March, more than 130 people have been martyred and thousands more injured by Israeli army fire during Palestinian protests against the decades-long Israeli occupation and 11-year blockade, which has gutted the coastal enclave's economy and deprived its roughly 2 million inhabitants of basic commodities.
With Israel focused on rising tension along its northern border in its efforts to prevent Iran from establishing a permanent military foothold in post-civil war Syria, it has been wary of escalating hostilities in Gaza.