"I think it's going to be very hard to put a ceasefire back together again if Israelis and the international community can't feel confident that Hamas can follow through on a ceasefire commitment," he told reporters.
Obama said the United States "unequivocally condemned Hamas and the Palestinian factions that were responsible for killing two Israeli soldiers, and abducting a third almost minutes after a ceasefire had been announced."
"I want to make sure that they are listening. If they are serious about trying to trying to resolve this situation, that soldier needs to be unconditionally released, as soon as possible," Obama said, addressing Hamas.
But the US leader added, "We have also been clear that innocent civilians in Gaza caught in the crossfire have to weigh on our conscience and we have to do more to protect them."
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"He has endured on many occasions really unfair criticism. Simply to try to get to the point where the killing stops," Obama said.
And he insisted it was "not particularly relevant" whether Hamas or another group was behind the reported kidnapping of the Israeli soldier.
"The point is, when they sign on to a ceasefire, they're claiming to speak for all the Palestinian factions. And if they don't have control of them, and just moments after a ceasefire is signed, you have Israeli soldiers being killed and captured, then it's hard for the Israelis to feel confident that a ceasefire can actually honored," Obama added.