The desperate residents of a besieged district of Damascus are expected to run out of food on Sunday, leaving 18,000 people facing starvation and leading relief agencies to declare the crisis "unprecedented in living memory".

Food packages have not been delivered to the Yarmouk Palestinian refugee camp for 10 days, and Syrian authorities are not expected to allow food trucks in over the Easter weekend. Residents have resorted to eating leaves and animal feed. Some say they cannot get access even to scraps, as a desperate blockade by government forces, in place for nearly 18 months, continues to cut off supplies.

Syrian officials have allowed only sporadic access to Yarmouk, to relief groups led by the UN Relief and Works Agency (UNRWA), since the first pleas for help from residents early last year.

"It is unprecedented in living memory for a UNRWA-assisted population to be subject to abject desperation in this way and the sheer humanitarian facts cry out for a response," organisation spokesman Chris Gunness told the Observer. "Without that, the humanity of all of us must be seriously questioned.

"It is an affront to all of us that in a capital city of a member state, women are dying in childbirth for lack of medical care, there are incidents of malnutrition among infants and people are resorting to eating animal feed."

Refugees queue for food parcels in Yarmouk in March. Photograph: Reuters

Once the biggest Palestinian camp in Syria, and held up as a beacon of the regime's support for the Palestinian cause, Yarmouk is now a husk, its bombed-out buildings home to an ever-decreasing number of desperate residents and opposition fighters. Several thousand Syrian citizens are also living among the Palestinians. They also remain without access to food supplies.

To keep the remaining residents from starving, UNRWA says it needs to deliver at least 700 food parcels per day, each of which feeds five to eight people. It has only managed to get in 100 per day on average since the start of the year. However, conditions have drastically worsened in recent weeks, with all supplies stopped amid regime demands that rebel groups inside surrender.

An agreement to allow unfettered access to Yarmouk, brokered in January between all sides including a Palestinian faction that supports the Syrian government, broke down last month. Ever since, Syrian troops have been on the offensive near the camp, which weaves into the south-western suburbs of Damascus.

"We've got nothing," said Abu Issa, 60, a resident of Yarmouk. "No food, no money. We are sharing the animals' food by living on grass we get from the gardens. The Syrian army do not allow anything to get in unless the rebels leave the camp and the rebels refuse to leave and we are stuck between. I have three sons, they were desperate to leave the camp by any means. A smuggler promised to take them out and then outside of Syria, but they were arrested at the first checkpoint and I know nothing about them, if they're dead or alive."

Bashar al-Assad. Photograph: AP

The crisis in Yarmouk is unfolding as new UN documents appear to support a widespread opposition claim that the regime of President Assad is using starvation tactics as a weapon of war. The documents, obtained by Foreign Policy magazine, track the success of the UN's world food programme in the two months since the UN security council passed a resolution demanding immediate humanitarian access to aid workers.

The documents show that more food parcels have reached those in need than before the resolution was passed, but that was due to families fleeing to regime-controlled areas where food is more readily available. Food has also remained critically short in other opposition-held parts of the country, including the Old City area of Homs, which has been under an unrelenting attack for six months.

Before the war, food and water were abundant in all parts of the country. However, areas far from the Turkish, Jordanian and Lebanese borders – which are still enjoying some cross-frontier trade – are now reporting increasing scarcity in places that rely solely on regime supply lines, including Homs. Indicators of malnutrition have risen substantially in recent months.

Valerie Amos. Photograph: Murdo Macleod

The UN under-secretary general for humanitarian affairs, Valerie Amos, has told the security council that 240,000 people remain besieged across Syria. Most have little access to essentials.

Staggering numbers continue to define the Syrian violence, which is now into its fourth year and shows little sign of abating. More than 9 million people are in need of constant humanitarian assistance, a similar number have been internally displaced, and more than 2 million have fled across borders. In addition, more than 150,000 people have been killed and large parts of the country destroyed.

The UN has made a series of strident statements, but the security council has remained largely unable to shape events, with Syrian allies Russia and China opposing measures to limit the regime's influence.

"Hundreds of people are killed with chemical weapons and the security council is able to adopt a robust approach," said Gunness. "Let us hope that when thousands are facing the threat of malnutrition and worse that the security council can be equally robust."