BAGHDAD — As U.S. warplanes tilt the battlefield against Islamic extremists in Kurdish-controlled territories, Iraqis in the rest of the country are growing resentful that the United States is not intervening more forcefully to protect Arabs who have been fighting extremists for months.

They see the United States wading in to protect a favored ally in Iraq’s Kurdish Regional Government, but leaving the rest of Iraq to fend for itself since extremists in the Islamic State displaced hundreds of thousands of Shiite Arabs when they seized the city of Mosul in June.

“From the beginning, the Iraqi government has asked America to step in to a dangerous situation for the Shiites,” said Farid al Ibrahimi, a Shiite lawmaker. “When (the Islamic State) tried to attack the Kurdistan region, the movement by the Americans was so, so, so fast.”

The Islamic State is retreating from its advance in the Kurdish north but continues to hold significant territory in the country’s Sunni Arab west and middle.

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Other factions in Iraq also are clamoring for more U.S. military assistance.

Some say they want Western forces to drive out the Islamic State because they don’t trust their own military not to inflict excessive collateral damage or to refrain from payback assaults on Sunni Arabs who stayed in territory held by the extremists.

“If America doesn’t help us, we will never go back,” said Bashir Hassan, 59, an Iraqi Turk who has been homeless for nearly two months since the Islamic State attacked his village near the city of Tal Afar.

He’s a Shiite Muslim who no longer trusts his Sunni neighbors since extremists moved into their community, and, he says, helped the Islamic State raid his home.

The extremist group’s high-water mark came Aug. 3, when it set off fears that it could hit the Kurdish capital of Irbil after an assault on the Kurdish city of Sinjar that drove tens of thousands of people into mountain hideouts.

The Kurds control a semiautonomous region in northern Iraq and they have long sought independence. They’ve been close U.S. allies since the Gulf War, when the United States created a no-fly zone that protected them from Saddam Hussein’s military.

On Sunday, U.S. jets hammered Islamic State positions near the Mosul Dam, clearing a path for Iraqi counterterrorism and Kurdish troops to retake a facility that powers Iraq’s second-largest city.

Closer to the capital, Baghdad residents have been bracing for attacks by the Islamic State since the group seized territory in Anbar province in January.

President Obama on Aug. 7 authorized U.S. airstrikes in Iraq to protect U.S. personnel and to support humanitarian measures intended to free members of the Yazidi religious sect who were trapped by the Islamic State after they fled Sinjar.

The order carried an implied agreement to protect Baghdad, which houses America’s largest embassy, but it did not explicitly authorize strikes elsewhere.

Obama told The New York Times that he did not order airstrikes sooner because he wanted to pressure Prime Minister Nouri al-Maliki’s supporters to choose a new leader who might nurture a more inclusive government.

Al-Maliki’s party has since selected lawmaker Haider al-Abadi to follow al-Maliki, opening the door to increased American military support.

U.S. officials have not described what kind of assistance they might offer, or said whether it would include airstrikes south of the Kurdish territory.

Shiites want a more explicit commitment now that they have rejected al-Maliki, as the Americans wanted.

“America is in charge of the defense of Iraq from whatever risk because America was the reason for the destruction of the infrastructure of Iraq and leaving the Iraqi army out of order, so they are obliged to protect Iraq,” said Razzaq al-Hadari, a Shiite lawmaker from the Badr Bloc.

He called the U.S. “somehow lazy” in its reaction to the Islamic State’s first assault on Mosul.

Sunni leaders, likewise, have been calling for more direct intervention from the U.S. military. Jamila al-Obeidi, a Sunni parliament member, wants U.S. assistance because she believes the Iraqi air force has hit too many innocents in its strikes.

Other Sunni tribal leaders have been seeking U.S. assistance to turn back extremists in their communities, an echo of the 2007 “Sunni Awakening” in Anbar Province when tribes worked with the U.S. military to expel al-Qaida fighters.

But some Iraqis are just as adamant that the United States should stay out of Iraq as they were during the American occupation.

“The Americans are our enemies,” said Abu Faroq Jumaili, a former Iraqi army lieutenant colonel during Saddam’s regime. He now leads fighters opposed to the Iraqi government in Anbar province.

He said U.S. bombs would fall on the very Iraqis who are now asking for more aid.

“How did they forget that the Americans hit and bombed their houses? They are not far away from an airstrike that will hit their houses again. We don’t trust the Americans,” he said.