The executive order signed on Friday banned nationals of seven mainly Muslim countries from the Middle East and Africa for 90 days but has sparked confusion in its interpretation.
Israel is home to around 140,000 people born in the seven countries covered by the decree, including about 45,000 from Iran and 53,000 from Iraq, according to official statistics.
Many fled persecution, and the majority are now over the age of 65.
The Israeli government had been seeking clarification as to whether they were included in the ban.
"If you have a currently valid US visa in your Israeli passport and were born in Iraq, Iran, Libya, Somalia, Sudan, Syria, or Yemen, and do not have a valid passport from one of these countries, your visa was not cancelled and remains valid," a US embassy statement said.
"We continue to process visa applications for applicants born in those countries, so long as they do not have a valid passport from one of those countries," it added.