The exchange of fire followed months of tension that has raised the prospect of a fourth war in the blockaded Gaza Strip since 2008.
Three people were wounded in Israel when a rocket struck the southern town of Sderot, police said.
The Gaza Health Ministry said the two, 15 and 16, died when the building they were standing near was hit.
Israel said it was focused on hitting militant targets and was warning Gaza civilians to keep their distance from certain sites.
Israel's political leadership is considering a range of possibilities for trying to halt the rocket fire, including targeted assassinations of Hamas terror chiefs, the use of ground forces, and a ceasefire mediated by Egypt and/or others, but no decision had been made as of Saturday late afternoon, Hadashot TV news reported.
Israeli warplanes targeted an under-construction building in al-Katiba neighborhood in Gaza on Saturday, the Palestinian Health Ministry said.
Qassem said that he had told the sides that Israel started launching the airstrikes on Gaza and it was the Israeli military that has to stop the strikes.
In a relatively rare admission, Hamas said it fired the rockets to deter Israel from further action.
The operation is one of Israel's broadest since the 2014 war with Hamas.
A spokesperson for the Israeli prime minister did not immediately comment on the ceasefire.
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Israel and Egypt said the blockade was a necessary security measure against militants.
"The protection and the defence of our people is a national duty and a strategic choice", Barhoum said.
Since protests and clashes broke out along the Gaza border on March 30, at least 141 Palestinians have been killed by Israeli fire, 50 of those belonging to Hamas.
On Friday, thousands of Palestinians gathered near the Gaza border for their near-weekly protest.
No Israelis have been killed.
Hamas called the move a "crime against humanity", with Gaza already suffering from deep poverty and worsening humanitarian conditions.
Early in the morning, the Israeli military said in a statement that at least one Hamas rocket landed inside a rural settlement in Sha'ar HaNegev Regional Council area.
Molotov cocktails, flaming tyres and stones were also hurled in the direction of its soldiers, according to the Israeli army. Most of the recent rockets from Gaza have been fired by smaller factions but Hamas spokesman Fawzi Barhoum said it was an "immediate response" that was meant to "deliver the message". Palestinians and rights groups say unarmed protesters are being shot while posing no real threat.
"The battalion command's entire infrastructure has been destroyed, vaporized, turned into a giant hole", said Israel Defense Force Spokesperson Brigadier-General Ronen Manelis.