More than two million people have already fled
Peter Kessler of the UN refugee agency (UNHCR) says that if the Taleban return stolen vehicles and allow staff still inside the country to carry out their work, much aid could still be distributed.
The UN's Children's Fund (Unicef) has warned that 100,000 more children may die in Afghanistan this winter unless aid reaches them soon.
Dr Eric Laroche of Unicef says worsening weather will compound the misery of those in need and many will freeze to death unless they get clothes, tents and blankets.
Heavy snow is expected soon, blocking roads that are used by lorries to supply aid.
UN officials said they would use bulldozers to keep the roads open for a few more weeks and would resort to air drops of snow-proof bags of food if necessary.
Mutual accusations
Mr Kessler spoke out after Taleban officials warned of a humanitarian crisis in Afghanistan and called on the UN and other agencies to help the thousands of people displaced by the US bombing.
The Taleban's representative in Pakistan, Mullah Abdul Salam Zaeef, had said the UN's reservations over the delivery of aid were politically motivated and the only threat came from American bombs.
But Mr Kessler said that the Taleban were failing to co-operate.
"The UNHCR and our partner agencies have had our vehicles stolen, our offices taken over and our staff beaten," he said.
"It has not been very easy to work inside Afghanistan in recent weeks.
"It has been the breakdown in law and order that has made it so difficult to distribute the aid and to maintain contact with our colleagues who remain in the country."
Guarantees needed
Mr Kessler said US bombing was another problem to the distribution of aid but "certain avenues" could be opened if the Taleban co-operated.
"There are hundreds of UN personnel still on the ground in Afghanistan and thousands of NGO employees still trying to carry out aid deliveries," he said.
"But the aid is not being delivered in the quantities needed. What we would like from the Taleban is the return of our offices and assets and a guarantee that our people on the ground won't be hassled by armed men."
Mr Kessler added: "The needs inside Afghanistan are absolutely enormous. People are suffering.
"Aid agencies need the environment in which to work, and right now it is mainly the Taleban who can give us that space."
Afghan refugees are said to be fleeing in growing numbers since the US refusal to suspend bombing for the Muslim holy month of Ramadan.
The Taleban call for aid came after a coalition of charitable groups urged the United States to respect humanitarian law in its war against terrorism, calling for "exceptional attempts to protect civilians".
The UN estimates that 5.3 million Afghans are in need of immediate humanitarian aid ahead of the harsh winter.