BAGHDAD >> Iraqi forces, backed by U.S. airstrikes and advised by U.S. officers, have been making strides in Anbar province, slowly taking back territory from the Islamic State.

But in Fallujah, a city in Sunni-dominated Anbar that has been in the hands of the Islamic State longer than any other in Iraq or Syria, civilians are starving as the Iraqi army and militias lay siege to the city. And elsewhere in the province, Shiite militias supported by Iran are carrying out kidnappings and murders and restricting the movement of Sunni Arab civilians, according to U.S. and Iraqi officials.

For seasoned observers of the U.S. military involvement in Iraq — going back more than 25 years to the start of the Persian Gulf war — it is all part of a depressingly familiar pattern: battlefield gains that do not bring stability in their wake.

“Unfortunately, as has been a trademark of U.S. involvement with Iraq at least since 2003 (and arguably since 1991), military success is not being matched with the commensurate political-economic efforts that will ultimately determine whether battlefield successes are translated into lasting achievements,” Kenneth M. Pollack, a senior fellow at the Brookings Institution and a longtime Iraq analyst, wrote recently in an online column.

A growing number of critics are warning that U.S.-backed military victories need to be backed up with political reconciliation between Sunni and Shiite Arabs, something Iran is working against, and with determined efforts to rebuild cities so that civilians can return. In Anbar, they note, the situation is bleak: Shiite militias have worsened sectarian animosities, and hundreds of thousands of civilians have been unable to return home.

More broadly, analysts and officials say, it has become clear that though the United States and Iran both want to defeat the Islamic State in Iraq, they have been unable to work together to promote unity in the country — even after a deal was reached last year over Iran’s nuclear program, which many hoped would allow them to cooperate more closely.

Nowhere is this dynamic more pronounced than in Anbar, a vast desert area of western Iraq that for years has been a homeland for the Islamic State and its forerunner, al-Qaida in Iraq, and where hundreds of U.S. soldiers and Marines were killed after the U.S. invasion of Iraq in 2003.

As the United States supports the Iraqi army and some local tribal fighters in battling the Islamic State, Iran has quietly pursued its objectives in the province, officials say. It wants to secure a land route to Syria and its allies, the government of President Bashar Assad and Hezbollah, the Lebanese Shiite movement, and to protect Baghdad and the Shiite-dominated south of Iraq.

The situation in Anbar has grown increasingly muddled as the Obama administration has stepped up its military support to Iraq, announcing that it will deploy Apache helicopters and position more troops closer to the front lines. It has touted victories in Anbar as an important step toward liberating the country from the Islamic State, also known as ISIS or ISIL, and as a prelude to a campaign, possibly this year, to retake Mosul, Iraq’s second-largest city.

But Iran’s proxies are undercutting efforts to unite the civilian population, a necessity if Iraq is to eventually extinguish extremism. In the siege of Fallujah, a Sunni city, the Shiite militias have prevented civilians from leaving Islamic State territory while resisting calls to allow humanitarian aid to reach the city. Sunni Arab civilians in the province are increasingly reporting kidnappings and murders by the militias, accounts that U.S. and Iraqi officials say are credible.

In some cases, after civilians have disappeared, their families have received ransom demands. Abu Abdulrahman, a resident of Amiriyat al-Fallujah, a city in Anbar under the control of the government, said three of his cousins vanished last year after being stopped at a militia checkpoint.

“We haven’t heard anything about them since then,” he said, although a man approached the family and demanded a ransom of $8,000, which was paid. “He disappeared with the money,” he said.

Conditions are so dire in Fallujah for the tens of thousands of civilians trapped there that dozens of people have starved to death, civilians and activists say. Food prices have skyrocketed, with a bag of flour that would cost $15 in Baghdad going for $750, Human Rights Watch has reported.

The rights group recently warned that if aid does not reach Fallujah, “the results for civilians could be calamitous.”

“We are profoundly worried about Fallujah,” Lise Grande, the U.N. humanitarian coordinator for Iraq, said in a recent statement. “There are reports of widespread food shortages and lack of medicines. We don’t have access to the city, but we have to assume based on what we are hearing that people are in terrible trouble.”

Hadi al-Ameri, a prominent Iraqi official who leads the Badr Organization, a long-standing militia backed by Iraq, said in an interview this year as the siege of Fallujah began that it was a military necessity to “surround the city, to cut off supply lines.”

When asked about the demand from the United Nations and other groups to find a way to send food in, he said, using another acronym for the Islamic State, “to give food to who — to Daesh?”

Inside Fallujah, some civilians who say they initially supported the Islamic State as preferable to the government in Baghdad now say they would welcome liberation. But they say they are caught between the Islamic State, which has become more brutal toward civilians as the siege has dragged on, and the government and militias.

“The situation inside Fallujah is difficult because of the siege imposed by the security forces outside Fallujah, and from the inside by ISIS, who won’t let us get out of the city,” said Ahmed Mohammed, a Fallujah resident reached by telephone.

Cellphone reception is spotty, and anyone seen talking on a cellphone is at risk of arrest. “It has become very difficult for us to use our mobile phones because ISIS expects that we may be talking with the government,” said Qais al-Jumayli, who was reached by phone last week. “Therefore, we are very cautious.”

He added, “We don’t know our destiny, or the destiny of our families.”