The Washington Post reported the killing of the six hostages increased the urgency among Mr Biden’s aides to push for a deal.
“You can’t keep negotiating this. This process has to be called at some point,” one senior official told the newspaper.
“Does it derail the deal? No. If anything, it should add additional urgency in this closing phase, which we were already in,” they added.
The US, Qatar and Egypt have for months tried to secure a deal that includes a ceasefire in Gaza and the release of the remaining hostages held by Hamas.
The Biden administration has criticised Hamas for failing to agree to a deal, though US foreign officials have also accused Mr Netanyahu of making demands that have also derailed efforts.
The war in the strip began after Hamas breached the Gaza border, killed 1,200 Israelis and abducted 251 on 7 October.
Israel has since killed over 40,000 Palestinians in retaliatory attacks, according to the Hamas-run Gaza health ministry.
The US response to the war has had implications for the Biden administration and Ms Harris, the Democratic nominee in November’s US presidential election. Pro-Palestinian factions in the party have urged for a ceasefire.
Ms Harris’s opponent, Republican nominee Donald Trump, has blamed Ms Harris and Mr Biden’s failure to secure a deal for the hostage deaths last weekend.
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