Many Muslims in the Middle East have reacted with a mix of caution, suspicion and scorn to Donald J. Trump’s election victory and his appointments of aides with hostile views toward Islam.

Struggling to understand what Mr. Trump’s ascent means for their war-ravaged region, some have expressed hope that he will confront militant Islamist extremists far more aggressively than the Obama administration has done.

But others fear Mr. Trump’s views will be exploited as a recruiting tool by the Islamic State and other violent militants.

In Iraq, whose modern history has been profoundly shaped by the decisions of American presidents, officials and citizens alike are weighing Mr. Trump’s harsh words against his promise to defeat terrorism.

Surprisingly, some Iraqis seem less offended by Mr. Trump’s comments linking terrorism to Islam than American liberals.

Iraqis have endured years of Islam being used to justify mass killing, and some see Mr. Trump as a truth-teller in calling out Islam — or a certain brand of it — as the problem.

Iraqi Shiites, in particular, say they believe Mr. Trump will take a harder line on Saudi Arabia, the regional Sunni power that many see as the incubator of the extreme form of Islam, known as 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 occupied parts of Iraq and Syria for the past two years. CONTINUE