Like many Israelis, Bronx-born Eli Knoller, who has dual citizenship and lives in an Israeli settlement in the West Bank, hopes the next American president allows Israel to “finish the job” against Hamas in Gaza, where his son was killed in battle.

Abduljabbar Alqam, a Palestinian American who lives just a few miles away, is horrified by what he calls U.S. complicity in the suffering of Palestinians in Gaza.

But they have at least one thing in common: Neither planned to vote for Vice President Kamala Harris. Mr. Alqam believes the Biden administration has been too supportive of Israel and the war in Gaza; Mr. Knoller believes it has not been supportive enough.

In the Israeli-occupied West Bank, tens of thousands of U.S. citizens live on opposing sides of one of the world’s most entrenched conflicts, and many are bitterly disappointed with the Biden administration’s approach to Israel’s war in Gaza, triggered by the deadly Hamas-led attack on Israel last October.

Opinion polls show that Israelis largely support former President Donald J. Trump, fondly recalling his near-unreserved support for a country now facing increasing international isolation, while many Palestinians are frustrated with President Biden’s backing for Israel and see little difference between the two candidates. Their frustrations reflect the wider discontent over the war in Gaza across the American political spectrum.