Iraqi Shiites say they believe Mr. Trump will take a harder line on Saudi Arabia, the Sunni power that many see as the incubator of the extreme form of Islam, Wahhabism, that forms a basis of the Islamic State’s ideology.

“The victory of Trump is the beginning of the end of extremist Islam and Wahhabism,” said Mouwafak al-Rubaie, an Iraqi lawmaker and the country’s former national security adviser.

In Mr. Trump’s vow to defeat terrorism many Iraqis say they have hope that decisive American power will be marshaled to eradicate the Islamic State, the extremist group also known as ISIS, which has brutalized parts of Iraq, Syria and Libya and plotted attacks on the West.

“We have no concerns about the policy of Trump because he is against extremism,” said Saad al-Hadithi, the spokesman for Prime Minister Haider al-Abadi of Iraq. “We think we are facing one enemy, and that is fighting ISIS. Therefore, I do not think there are fears or concerns about a new American policy.”

On Friday, Mr. Abadi spoke by phone with Mr. Trump for the first time, and a statement released by the prime minister’s office said the two leaders affirmed their cooperation against the Islamic State. Mr. Trump told Mr. Abadi, “you are essential partners to us and you will find strong and deep support.”

But Mr. Trump’s invective against Muslims during the campaign, and his apparent intent to put those feelings into policy with his appointments, represented a deep betrayal to the many Iraqis who worked as translators alongside the American military in Iraq, and have dreamed of immigrating to the United States under a special visa program that will now be in jeopardy.

“Though six years have passed, I was still hoping to get a call at any moment that would represent the fulfillment of the promise they made to me,” said Ali Najam Abdullah, who worked as an interpreter for the American military in Anbar Province for five years.