US troops have directed the convoy, carrying emergency food, water and medical supplies into the Falluja hospital on the outskirts of the town, away from the reach of local citizens.
"They will not be allowed to cross the bridge today," Captain Adam Collier said at Falluja hospital, where the convoy is waiting to cross the Euphrates River into the main part of the embattled Iraqi city. He cited security reasons.
Abu Fahd, a member of the relief convoy, told Aljazeera "the relief convoy wants to enter Falluja town for humanitarian purposes only, to save women, children and elderly people".
"I hope the United Nations will hear our appeals," he said.
"We are now in Falluja hospital, outside the city. There is no one in the hospital except the medical team, doing nothing."
But the US military said it saw no need for the Iraqi Red Crescent to deliver aid to people inside Falluja and said it did not think any Iraqi civilians were trapped inside the city.
"There is no need to bring [Red Crescent] supplies in because we have supplies of our own for the people," said US marine Colonel Mike Shupp.
The relief convoy aims to help
civilians stuck in Falluja
"Now that the bridge [into Falluja] is open I will bring out casualties and all aid work can be done here [at Falluja's hospital]," he added.
He said he had not heard of any Iraqi civilians being trapped inside the city and did not think that was the case.
But aid workers say there are still hundreds of families left in the city, which has been pummelled by sustained aerial bombardment and artillery fire in recent days.
"We know of at least 157 families inside Falluja who need our help," said Iraqi Red Crescent spokeswoman Firdus al-Ubadi.
The aid group sent seven trucks and ambulances to Falluja on Saturday, hoping to get food, blankets, water purification tablets and medicine to hundreds of families trapped inside the city during the previous six days of fighting.
"There is no need to bring [Red Crescent] supplies in because we have supplies of our own for the people"
US marine Colonel Mike Shupp
"None of the injured residents are being allowed to come to the hospital, while those outside are not allowed to go into the town," Abu Fahd said.
"The town is suffering from cuts in power and water supplies. There are no medicines or ambulances either.
"The injured and the dead are now on the streets. Many families want to get out of their houses, but they have no alternative shelters to go into," he said.
"The US forces have prevented us from entering the town claiming it is not safe. US forces have said they control 80% of the town."
"I have asked them [US-led forces] to allow the relief team into the areas they control, to offer humanitarian aid for women, children and the elderly, and transfer the injured to the hospital, but they have refused," Abu Fahd said.
Baghdad hospitals have received
wounded refugee children
Red Crescent's al-Ubadi said: "They are dying of starvation and lack of water, especially the children.
"If there is no solution to this crisis it will expand to other cities and other parts of Iraq and there will be a great disaster here."
Earlier, the Red Crescent society despatched a convoy of four relief trucks and an ambulance to Amiriyat al-Falluja and a tourist village in Habbaniya, where an additional 1500 refugees are camped.