An aid convoy managed to deliver food to hunger-stricken Eastern Ghouta on Friday despite renewed bombardment by Syrian regime forces who have seized more than half of the besieged rebel enclave.
A previous delivery of aid to the region was cut short amid shelling.
"A case in point is the United Nations and partners inability to return to Douma in east Ghouta today because the movement of the convoy was not authorized due to security concerns on the ground", she said.
"They are in", ICRC spokeswoman Ingy Sedky said of the 13 trucks loaded with 2,400 food parcels that had been waiting outside the enclave east of Damascus after the interruption of Monday's delivery.
Jan Egeland says it is "impossible" to cross into the frontline and deliver aid to people "we know are on the starvation point" because of the current fighting, which he describes as possibly the worst ever in the besieged Damascus suburb.
In less than two weeks, the Syrian army has retaken almost all the farmland in Eastern Ghouta, under cover of near-ceaseless shelling and air strikes, leaving only handful towns - about half the enclave - still under rebel control.
The onslaught has killed more than 1,000 people, the medical charity Medecins Sans Frontieres (MSF) said on Thursday.
Early Friday, the air strikes stopped briefly, with the area seeing its calmest night in more than a week, according to the Britain-based Syrian Observatory for Human Rights monitoring group.
"The situation is relatively good today".
"We were taken aback by the fighting that broke out despite guarantees from the parties involved in this conflict that humanitarians could enter Douma, in Eastern Ghouta", said ICRC regional director Robert Mardini.
Medical facilities have been hit in air strikes, adding to shortages of equipment that have made it harder to treat the wounded.
Rebels deny this and say the area's inhabitants have not crossed into government territory because they fear persecution.
The Army of Islam said that the detainees from the al-Qaida-linked Levant Liberation Committee have asked to be sent to the rebel-held province of Idlib in Syria's northwest.
Government forces this week advanced from the east and were less than a mile away from linking with forces on the western side of eastern Ghouta and cutting the rebel-held district in half.
The two allies accuse the Syrian rebels of shooting at civilians to prevent them from fleeing the fighting into government areas.
A United Nations official who entered eastern Ghouta earlier this week said civilians stuck inside the enclave - mostly women and children - would like to leave have nowhere to go and feel they can't exit safely from the designated checkpoints.
The terror of the bombardment and the increasingly unbearable living conditions may push people to fearless the fighting and flee, according to one resident of Douma.
"They are putting pressure on the civilians and luring them out (of eastern Ghouta)".
The WHO has counted 67 attacks on medical units so far in 2018 - roughly half as many as all of previous year, according to the organization's spokesman Christian Lindmeier.
Pro-government forces, led by the Syrian Army's fourth armored division and Republican Guard, are advancing towards the area after successfully repelling a militant counter-attack, and subsequently seizing nearby farms.