Iran is among seven countries whose nationals are barred from entering the United States for 90 days under Trump's order.
"The US decision to restrict travel for Muslims to the US, even if for a temporary period of three months, is an obvious insult to the Islamic world and in particular to the great nation of Iran," the statement said.
"Despite the claims of combating terrorism and keeping American people safe, it will be recorded in history as a big gift to extremists and their supporters."Iran's ban will remain in place until Trump's order is lifted, the statement said.
The other six countries listed in the executive order are Iraq, Syria, Libya, Somalia, Sudan and Yemen. Other nations may be added. The order exempts diplomats and members of international organizations from the ban.
The executive order also stops the admission of all refugees to the United States for four months.