The Israeli military last reported fire from Gaza around 1:30 a.m., and said special orders put in place in southern Israel over the weekend, including a prohibition on large gatherings, had been lifted.
Israeli aircraft struck militant targets in the Gaza Strip and Palestinians launched dozens of mortar bombs and rockets from the enclave into Israel on Saturday, the Israeli military said.
Hamas does not recognise Israel's right to exist but a year ago said it was ready to accept an interim Palestinian state limited to Gaza and the West Bank.
Russian President Vladimir Putin, right, shakes hands with Israeli Prime Minister Benjamin Netanyahu during their meeting at the Kremlin in Moscow on July 11.
'They were crowned by the success of the Egyptian effort to restore calm and end the escalation'.
The Palestinian Islamic Jihad militant group said in a separate statement that a truce had been reached.
A senior Israeli defence official said: 'Only the facts on the ground will dictate our further response'. There were no reports of an Israeli counter-attack in Gaza.
The Health Ministry in Gaza said the teenagers, aged 15 and 16, were killed by shrapnel from an Israeli attack on the training facility.
After several balloons drifted into Israel Sunday, the military said it targeted the Hamas squad that had launched them from the northern Gaza Strip.
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"We are talking about the biggest offensive strikes since Protective Edge", Brigadier General Tzvika Haimovic told journalists, referring to Israel's name for its 2014 operation in the Gaza Strip.
Israel's army said Saturday's strikes targeted military facilities belonging to Hamas.
"The action we are taking draws a clear red line: that from now on, we will not allow this". Striking in the heart of Gaza City is typically only seen during full-blown conflicts like the 2014 war and could signal that a further escalation may be in store.
"The focus of the attack is a wide-scale strike of the Hamas Battalion HQ in Beit Lahia, which includes urban warfare training facilities, weapon storage warehouse, training compounds, command centers, offices and more", the IDF said in a statement.
Gaza's health ministry said Saturday that a 20-year-old struck by gunfire Friday during the protests in the southern Gaza Strip had also died of his wounds.
The United Nations' Middle East envoy Nickolay Mladenov was in Gaza and "working with all concerned parties to de-escalate the situation", a UN official said on condition of anonymity. Nearby houses were damaged.
"Troops responded by firing towards the terrorists", the military said. The IDF retaliated against the most recent attack.
The IDF said that building was hit only after its residents were warned in advance to leave.
Sporadic Palestinian rocket attacks and incendiary kites from Gaza that have burned large tracts of farmland in Israeli border areas have increased public pressure on Netanyahu for a stronger armed response. 'Bombardment for bombardment, ' he said.
The Israeli military lifted its restrictions along the Gaza border Sunday, indicating it had accepted an Egypt-mediated cease-fire that ended a 24-hour round of fighting with Hamas militants that had threatened to devolve into all-out war.