President Biden pressed Prime Minister Benjamin Netanyahu of Israel on Friday to agree to the creation of a Palestinian state after the war in Gaza is over and raised options that would limit Palestinian sovereignty to make the prospect more palatable to Israel.

Hoping to overcome Mr. Netanyahu’s strenuous resistance, Mr. Biden floated the possibility of a disarmed Palestinian nation that would not threaten Israel’s security. While there was no indication that Mr. Netanyahu would ease his opposition, which is popular with his fragile right-wing political coalition, Mr. Biden expressed optimism that they may yet find consensus.

“There are a number of types of two-state solutions,” the president told reporters at the White House several hours after the call, their first in nearly a month amid tension over the war. “There’s a number of countries that are members of the U.N. that are still — don’t have their own militaries. Number of states that have limitations.” He added, “And so I think there’s ways in which this could work.”

Asked what Mr. Netanyahu was open to, Mr. Biden said, “I’ll let you know.” But he rejected the notion that a so-called two-state solution is impossible as long as Mr. Netanyahu is in power — “no, it’s not” — and he brushed off the idea of imposing conditions on American security aid to Israel if the prime minister continues to resist.

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