A year later, Hamas drove the Fatah-dominated Palestinian Authority entirely out of Gaza in four days of street battles, leading Israel to cut off all shipments in and out except basic food, humanitarian aid and urgent medical supplies.

Hamas declines to recognize Israel’s right to exist, renounce violence or accept previous accords signed between Israel and the Palestinian Authority. The diplomatic group known as the Quartet, made up of the United States, Russia, the European Union and the United Nations, has said that until Hamas meets those requirements, the Quartet will not deal with it.

But the world powers have grown increasingly disillusioned with the blockade, saying that it has created far too much suffering in Gaza and serves as a symbol not only of Israel’s treatment of Palestinians but of how the West is seen in relation to the Palestinians.

“Gaza has become the symbol in the Arab world of the Israeli treatment of Palestinians, and we have to change that,” the senior American official said. “We need to remove the impulse for the flotillas. The Israelis also realize this is not sustainable.”

At a meeting of the Quartet a year ago in Italy, for example, the group asserted that the current situation was not sustainable and called for the unimpeded provision and distribution of humanitarian aid within Gaza, as well as the reopening of crossing points.

But Obama administration officials made it clear that the deaths had given a new urgency to changing the policy.

Pressure against the blockade continued to grow on Wednesday: Turkey, which withdrew its ambassador to Israel after the raid, said full restoration of diplomatic ties was contingent on an end to the blockade.