A Red Crescent team delivered food and water to five families in a battered northern Falluja neighbourhood on Thursday after US marines patrolling the area found them hiding in their homes.
The organisation estimates that only 150 to 175 families stayed in Falluja after the start of the US-led offensive on 8 November, and civilians living in the ruined city have become desperate for water and blankets.
Red Crescent officials met on Thursday with US marine Lieutenant-Colonel Gary Montgomery to discuss cooperative aid efforts.
Aid convoys were able to enter Falluja on Wednesday and Monday, but only toured the town, and were unable to move freely and find any of the civilians who needed assistance.
Red Crescent efforts to assist civilians still in Falluja have been frustrated by ongoing military operations, and the agency's coordinator for Falluja, Jotiar Nafaa, says getting into the town to assess how many people need help is the main priority.
"It should start going better," Montgomery said after Thursday's meeting. "We weren't getting the information we needed from them so they weren't getting what they needed from us and were getting frustrated."
Speaking to Aljazeera on Thursday, Dr Rafia al-Isawi, the director of Falluja General Hospital, urged all physicians working in the town to resume work to help victims of the latest fighting.
"A number of hospitals which are determined to be rehabilitated are in need of medical teams," he said.
Meanwhile, there are increasing concerns for Falluja residents who left the town before the devastating US offensive.
Shaikh Muhammad Shawki al-Abdali, who lives in a cluster of hamlets just outside Falluja, said many of the 250 families who sought refuge in his village did not have shelter.
"I cannot bear to see their suffering any more, it causes me too
Shaikh Muhammad Shawki al-Abdali, village imam near Falluja
The villagers of nearby al-Subaihat said they welcomed the displaced with open arms.
"Friends of mine gave these poor people a room in their house, others gave them mattresses and food," 25-year-old Khalid Jiad said.
"But now there isn't much we can still do for them because we barely have any sugar, flour and rice left. We are almost in the same state as them."
A humanitarian convoy from an organisation calling itself the
Human Relief Foundation entered al-Subaihat for the first time on Tuesday and delivered 400kg each of rice and flour, 80 containers of oil and 25 tents.
The convoy's visit was a pleasant surprise for the villagers,
who had been cut off from the rest of the world since the start of the onslaught more than two weeks ago.
"I am really delighted that a humanitarian organisation was able to come here and I hope that the displaced will be able to return to their homes soon. I cannot bear to see their suffering any more, it causes me too much pain," Shaikh al-Abdali said.
In another development, a convoy including humanitarian supplies arrived at the Iraqi town of Saqlawia on Thursday.
The Red Crescent's work had
been hindered by the fighting
Many Falluja residents fled to nearby Saqlawia after the US-led offensive began, and the town is still receiving refugees.
The convoy included aid sent by the interim Iraqi government, Qatar and Bahrain.
Humanitarian relief inside Falluja and in nearby villages has
been impeded by smouldering violence, as US and Iraqi forces wrap up what was the largest post-war military operation in Iraq.
US marines have hinted that it could take more than two months to restore basic services such as water and electricity in the devastated town.