Nur Hassan, 30, and her daughter Rahaf Hassan, 2, were killed when their house in northern Gaza Strip sector Zeitun was demolished by the Israeli attack, medics said, with three others still trapped under the ruins.
Israel said it had targeted "two Hamas weapon manufacturing facilities" in response to two rocket launches at Israel yesterday, as well as a number of attempts by Palestinians to violently break into Israel from Gaza.
While Prime Minister Benjamin Netanyahu and president Mahmud Abbas have sought to avoid an escalation, frustrated Palestinian youths have defied efforts to restore calm and a wave of stabbings has spread fear in Israel.
Gaza had been mainly calm amid the week's unrest elsewhere, but the recent clashes, rockets and air strike exacerbated fears that a wider Palestinian uprising, or intifada, could erupt.
The Friday border clashes came as Hamas's chief in Gaza, Ismail Haniya, called the overall violence an intifada and urged further unrest.
Abbas as well as Netanyahu meanwhile spoke with US Secretary of State John Kerry, each putting the blame for the situation on the other.
Netanyahu said he told Kerry he expected the Palestinian Authority to stop its "wild and mendacious incitement, which is causing the current wave of terrorism".
And Abbas said he reiterated the need for Israeli authorities to stop giving cover to "settler provocations, carried out under the army's protection".
Kerry had shared his "deep concern" over the violence in separate conversations with the two, his office said in a statement, and "stressed the importance of upholding the status quo in word and deed at the al-Haram al-Sharif/Temple Mount and of preventing inflammatory rhetoric and actions that will increase tensions."
Clashes rocked West Bank cities Ramallah and Bethlehem yesterday.
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