The executive order signed on Friday banned nationals of seven mainly Muslim countries for 90 days but has sparked confusion in its interpretation with people unsure whether they can travel.
Israel is home to around 140,000 people born in the seven countries covered by the decree, including around 45,000 Iranians and 53,000 Iraqis, according to official statistics.
The majority are over the age of 65 and many fled persecution. Their Israeli passports say where they were born.
The Israeli authorities were also seeking clarification, foreign ministry spokesman Emmanuel Nahshon told AFP.
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Michael Wildes, a partner at the Wildes and Weinberg immigration law firm in the US and a former public prosecutor, said the wording of Trump's order was unclear.
He explained that the order refers to "aliens from countries" but does not explain how citizenship is defined.
"Either Congress is going to legislate or the president is going to clarify the executive order but until then I advise anybody who hails from those countries against travelling."
Meir Javedanfar, an Iranian-born Israeli and professor of Iranian politics at Israel's IDC Herzliya University, said Israelis born in those countries were "concerned" by the uncertainty.
"It shows the chaos and lack of preparation (in the US)."
Britain announced late Sunday its citizens had been given a partial exemption from the ban, allowing them to travel even if they originally come from one of the seven countries.
The clarification came after Mo Farah, a Somali born four-time British Olympic gold medalist, was advised he might not be able to return to his home in the US despite not having Somali citizenship.
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