The attack, which also injured their mother, took place near an Israeli settlement in the Jordan Valley and the girls' father witnessed the incident from a separate car following behind, local officials said.
In London, the Foreign Office confirmed the deaths and appealed for all sides in the Israel-Palestine dispute to de-escalate a situation which has seen violence flare up in recent days.
The family were residents of the Efrat settlement, near the Palestinian city of Bethlehem, according to Oded Revivi, the settlement's mayor.
He said: "With great sorrow we received an update on a shocking terrorist attack in which terrorists shot a car including a mother and her two daughters, residents of Efrat.
"The two girls were murdered and the mother is in (a) critical condition and we all pray for her quick recovery.
"The father of the family who drove in another car from the front turned around and witnessed the efforts to take care of his wife and daughters."
The cross-border fighting, while Jews are celebrating the Passover holiday and Muslims are marking Ramadan, erupted following violent scenes at Jerusalem's Al-Aqsa Mosque.
The Israeli strikes in southern Lebanon came after militants fired nearly three dozen rockets from there.
The Israeli military said it targeted installations of the Palestinian militant group Hamas in Lebanon.
Mr Cleverly said both sides in the Israel-Palestine dispute should "recommit themselves to a negotiated settlement".
He said: "The UK condemns the indiscriminate rocket attacks from southern Lebanon and Gaza and recognises Israel's right to self-defence.
"Now is the time for all parties across the region to de-escalate tensions.
"At the convergence of Passover, Ramadan and Easter, the UK calls for all parties to respect the historic status quo arrangements at Jerusalem's holy sites and cease all provocative action.
"The UK is a strong supporter of freedom of religion or belief and calls for places of worship to be respected.
"We value Jordan's important role as custodian of the holy sites in Jerusalem and condemns the Israeli police violence at the Al-Aqsa Mosque.
"When Israeli security forces conduct operations, they must ensure they are proportionate and in accordance with international law."
In Jerusalem, violence flared again at the Al-Aqsa Mosque before dawn prayers, with Israeli police stationed at one of the gates forcibly dispersing vast crowds of worshippers who chanted praise for Hamas.Â
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