BEIRUT — As Iraqi security forces choke off Islamic State fighters in the militant-held city of Fallujah, civilians inside say they are trapped and struggling to survive.

The military siege, which has tightened in the past two months, is preventing food and medical supplies from reaching the city 40 miles west of Baghdad, while the Islamic State won’t let families leave.

The United Nations says it is ‘‘deeply worried’’ about the deteriorating humanitarian situation and unverified reports of deaths from a lack of food and basic medicine.

Between 30,000 and 60,000 people are estimated to remain in the city, which has been under Islamic State control for more than two years. Their worsening plight comes amid an international outcry over starvation in the besieged Syrian town of Madaya — a disaster residents and officials from Fallujah say they fear could also unfold there if civilians aren’t evacuated.

‘‘We are frustrated, desperate, and afraid,’’ said a 32-year-old Fallujah resident who spoke on the condition of anonymity for fear of reprisals by the Islamic State. ‘‘There is hunger, lack of food, and lack of medicine.’’

Fallujah, which once had a population of more than 300,000, was the scene of some of the United States’ bloodiest fighting during the Iraq war, when Marines battled Al Qaeda in the city’s streets. It was the first city in the country to fall to the Islamic State militants at the beginning of 2014.

Washington Post