But it is unclear how Abbas, the Fatah leader, would be able to assert control over the crossing with Egypt, given opposition from Hamas, which seized the coastal territory in June and blasted open the Egyptian border wall last week in defiance of an Israeli-led blockade.
Tensions along Gaza's frontier with Egypt flared anew Tuesday when Egyptian forces tried to prevent Palestinian vehicles from driving into Egypt.
Hamas gunmen intervened, firing into the air to clear the way for cars to pass. They threatened to blast new holes in the border if Egyptian forces refused to back down.
Under heavy international pressure to ease its cordon, Israel has allowed European-funded fuel to reach Gaza's main power plant, but the main UN aid agency said its food shipments had been blocked for nearly a week.
Abbas won backing from the United States and European and Arab nations Monday for taking control of Gaza's only border crossing with Egypt, but he has faced resistance from Israel.
"If all of them want it, we will not be the ones that will undermine it. So it will happen," an Israeli official familiar with the deliberations said. "Given that we see Abbas as the legitimate force and we don't want to weaken him, we have no reason to prevent it."
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