On a campaign stop in Iowa, Trump was responding to the Hamas killing of at least 1,300 Israelis that triggered a war in which Palestinian health officials say Israel has killed more than 2,800 Palestinians in Gaza.

Trump, president from 2017-2021, said that if elected to a second White House term he will ban entry to the U.S. of anybody who does not believe in Israel's right to exist, and revoke the visas of foreign students who are "antisemitic."

He also vowed to step up travel bans from "terror-plagued countries." He did not explain how he would enforce his demands, including the one requiring immigrants to support Israel's right to exist under what he called "strong ideological screening."

Many of Trump's immigration policies were challenged in court during his presidency and his newest pledges could also face challenges.

A ban he imposed on immigrants from some Muslim-majority nations was struck down in lower courts but ultimately upheld by the U.S. Supreme Court. Biden ended that ban when he took office.

Trump said on Monday he would ban immigrants from Libya, Somalia, Syria and Yemen "or anywhere else that threatens our security". Trump also read a poem that he used to liken immigrants to deadly snakes.

Jaime Harrison, chair of the Democratic National Committee, described Trump's pledges as Islamophobic, extreme and designed to exploit "fear and anxiety."

Iowa is one of the earliest states to hold a Republican presidential nominating contest. A tough approach to immigrants was a cornerstone of Trump's first term as president.

He is the frontrunner to win his party's White House nomination and take on Democratic President Joe Biden in the November 2024 election.

Promising to drastically tighten U.S. immigration laws, Trump said: "If you want to abolish the state of Israel, you're disqualified, if you support Hamas or the ideology behind Hamas, you're disqualified, and if you're a communist, Marxist, or fascist, you are disqualified."

Most of Trump's Republican rivals have condemned Hamas and offered full-throated support for an expected Israeli invasion of Gaza, but none has laid out such a tough series of proposals to keep people out of and expel Hamas sympathizers from the U.S.

The United States along with several other countries have designated Hamas a terrorist organization.

Florida Governor Ron DeSantis, one of Trump's Republican rivals for the presidential nomination, said on Monday he favored the deportation of foreign students who support Hamas and would bar Gaza refugees from the U.S. if elected president.

Trump last week accused Israeli Prime Minister Benjamin Netanyahu of being unprepared for the Hamas attacks and called Hezbollah - the Iran-backed Lebanese militant group - "very smart."

His Iowa remarks appeared to be an effort in part to blunt that criticism.

"We will aggressively deport resident aliens with jihadist sympathies," Trump said.