ABU JASSIM can only afford to provide one meal a day for his seven-member family — usually a stew made of locally grown leafy green vegetables or rice with a small portion of flat bread. "We are experiencing the agony of starvation for the first time in our life," said Abu Jassim, a 52-year-old grocer and resident of the besieged city of Fallujah. In reality, nobody seems to be starving in Fallujah just yet. But medical officials say malnutrition is on the rise and vital medical supplies are running out. Since August, Iraqi government troops have tightened their grip around Fallujah — under Daesh (the so-called Islamic State) control since the early days of 2014 — and have prevented the entry of food and medicine into the city. Those seeking to flee the city have sometimes found themselves trapped by the militants, who seek to retain Fallujah's civilian population as human shields against a full-scale government assault. Several Fallujah residents spoke to The Associated Press over the telephone — all on condition of anonymity for fear of IS reprisal. Abu Jassim would only be identified by his Iraqi societal nickname, which translates as "Jassim's father." These residents depicted a bleak picture of conditions inside the city, with prices soaring for some basic staples while other items have completely run out. A 100-kilogram bag of flour now costs nearly 2 million Iraqi dinars ($1,550), compared to around 51,600 dinars ($40) in the past. Vegetable prices have risen by 500 percent and a 450-gram can of powdered baby formula has jumped from 3,870 dinars ($3) to 144,000 dinars ($112). Items like sugar and tea are simply not available at any price. Some residents, however, pointed out that families connected to IS members appear to suffer the least and receive extra provisions. There is also a severe shortage in medicine mainly for chronic diseases such as high blood pressure and diabetes, according to a doctor at the city's hospital. He added the majority of those seeking treatment these days are children and the elderly suffering from malnutrition. Alarmed by the deteriorating conditions inside Fallujah, the New York-based Human Rights Watch called on warring parties to make sure that aid reaches the civilian population. "The humanitarian picture in Fallujah is bleak and getting bleaker," Joe Stork, HRW's deputy Middle East director, said in a statement issued early this month. "Greater international attention to the besieged towns and cities of the region is needed or the results for civilians could be calamitous." The Daesh militants who control the city have taken steps to mitigate the shortages in the face of rising public frustration. In August, they opened a bakery to sell subsidized bread, but eventually had to close it due to a shortage of flour. Then they confiscated wheat stockpiled by farmers and started distributing five kilograms of flour to each family for free. But the residents complained that the quality of the flour was substandard since the wheat had been in storage for a long time and was meant to be used as animal fodder. Shortly after Fallujah fell into IS hands in 2014, Abu Jassim and his family joined thousands of residents fleeing the city. They settled in the northern city of Kirkuk, but returned home months later due to high rents and cost-of-living. In 2015, the militants began preventing civilians from leaving Fallujah. Anbar councilman, Falih Al-Issawi, estimated that about 90,000 individuals are now living in the city — down from approximately 300,000. Back in Fallujah, Abu Jassim started stockpiling food in 2015 after government forces, backed by US-led coalition airstrikes, began retaking key areas around the city and shutting down supply routes. "But that stock ran out by the end of December and things started to get worse in January as it was very cold," he said. Residents living across the Euphrates River in neighboring Khaldiya have tried to float supplies over the water to friends and relatives inside Fallujah — stuffing dried food and medicine into plastic bottles and gas cans. But residents say Daesh militants often confiscate these goods. Now Abu Jassim sets traps on his roof to capture pigeons and boil them down to make porridge, a dish his children do not like much. He also smashes date seeds and mixes them with flour. "We are waiting for salvation to see Fallujah liberated," he said. He may be waiting a long time. Fallujah is regarded as one of the toughest challenges for government forces seeking to retake territory from the Islamic State group. The city is one of the epicenters of Sunni Muslim resentment toward the Shiite-led government in Baghdad that took power after the 2003 US-led invasion to oust dictator Saddam Hussein. Fallujah remains strongly associated with the Sunni insurgency that erupted after Saddam's ouster, and it was one of the primary strongholds for Al-Qaeda in Iraq — the predecessor to the Islamic State group. It famously endured two bloody battles with US forces in 2004 after insurgents strung the charred bodies of four Blackwater security guards from a bridge over the Euphrates that same year. Even now, many Fallujah residents remain loyal to the Islamic State group and view it as the defender of the rights of the oppressed Sunni minority. "We are freed now, no army and arrests," said a 72-year old man who identified himself over the phone as Abu Rami. "Yes, we are living under siege and airstrikes, but we can eat anything available, not necessarily specific things ... Thank God, the Islamic State has not let us down and is looking after us." Abu Rami said one of his sons was arrested in 2010 and two others have joined the ranks of Islamic State fighters. "Before we had food and drink without dignity, and now we have dignity but with little in food and drink," he said.