BAGHDAD—As the Obama administration contemplates a broader military intervention in Iraq, some policy makers are focusing on a blighted collection of Shiite villages besieged for months by the Sunni insurgent group Islamic State.

Human-rights groups say some 17,000 people in the town of Amirli are facing an imminent threat similar to the recent siege of the Yazidi religious minority, a crisis that helped draw the U.S. back into military action in Iraq. Armed civilians and local police have spent the past 70 days fighting off the militants who have surrounded their villages.

Despite regular airdrops of food and ammunition from the Iraqi military, residents face desperate hunger and disease from drinking dirty river water. Their electricity and water have been cut off, and there is a severe lack of food and medicine.

"The U.S. deals in double standards in its defense and airstrikes," said Adel al Bayati, the town's district manager who has spent weeks appealing to Iraqi, Kurdish and American authorities to come to the rescue. "Our district might be the only one that has resisted since the crisis in June."

The plight of the Shiite villages, about 100 miles north of Baghdad, is among several crises the U.S. is evaluating to gauge whether American airstrikes could help. But so far, no plans have been presented to the Pentagon for an imminent operation, according to Defense Department officials.