Of the seven Israelis injured in the house on an agricultural community, three were children and all were members of one family.
And on Saturday, the Israeli army launched two separate air strikes against groups of Palestinians in Gaza who had allegedly flown balloons rigged with explosives into Israel.
Hamas issued a more muted response following the Ketziot Prison incident, calling on the global human rights organizations to intervene in the way Israeli security forces treat Palestinian prisoners and to protect them from "the ongoing Israeli crimes".
"This was a criminal attack on the State of Israel, and we will respond with force", said Netanyahu, who is also the defense minister, in a short video clip from Washington.
However, Israel has shut down its crossings into Gaza and has announced it is limiting the fishing zones off the coast in the Strip.
The BBC's Yolande Knell in Jerusalem says the latest rocket fire has dramatically raised tensions in the region, just two weeks before Israel holds a general election. "In a few hours I will meet with President Trump".
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The official declined to address whether there had been any consideration of the impact this could have on the Israeli elections. A year ago the USA moved its embassy from Tel Aviv to Jerusalem and backed Israel's assertion that the city is its capital.
Magen David Adom rescue service said it was treating six people after a house was struck.
Netanyahu, who is in the United States, said he would be cutting short his U.S. visit and would return home.
"The launch was carried out by Hamas from one of its positions in the Rafah area", Israeli army spokesman Ronen Manelis said.
Hamas claimed on Arab TV networks that the rocket was sacked "by mistake", possibly caused by the stormy weather, echoing a similar claim from 11 days ago when it fired two long-range rockets at Tel Aviv, an attack which elicited a broad Israel Air Force (IAF) strike on some 100 terror targets in Gaza. The territory is home to other armed groups, including Islamic Jihad, an Iranian-backed organisation that also has a formidable rocket arsenal.
The attack on the farming town of Mishmeret came at a time of tension shortly before the anniversary of Gaza border protests at the weekend.
An informal truce between Hamas and Israel had led to relative calm along the border of the blockaded strip, but recent weeks have seen another uptick in violence.