Israel's Prime Minister Benjamin Netanyahu said every Hamas member was "a dead man" after the first meeting of his country's emergency government, reports BBC.
Opposition figure Benny Gantz said it was "a time for war".
But US President Joe Biden said he had spoken to Netanyahu and made it clear that Israel must "operate by the rules of war".
Biden said he understood the anger and frustration of the Israeli people but urged Israel to adhere to the principles of the Geneva conventions. He also warned Iran - which has welcomed the Hamas attack - to "be careful".
Earlier on Wednesday Netanyahu and Gantz agreed to put aside a bitter political rivalry that had escalated into widespread protests.
Gantz told Israeli citizens that the newly-formed government was "united" and ready to "wipe this thing called Hamas off the face of the Earth".
"During the war period, no bills or government decisions will be promoted that do not concern the conduct of the war," said a statement.
Bd-pratidin English/Golam Rosul
