One aid worker said: "They are being stopped from leaving. We are not quite sure who is to blame.
"Maybe to have humanitarian aid workers in Kilinochchi is a way to put pressure on the government."
The convoy of vehicles carrying 141 mostly local staff from foreign and local aid agencies was stopped as it tried to leave the Tigers' northern base of Kilinochchi, officials said.
Rebel media coordinator Daya Master said the aid worker convoy was unable to leave because the crossing points into government areas were shut. He denied that the Tigers were stopping them and said they were free to go.
The military said it would allow the aid workers through if they are able to reach a crossing point in the northcentral district of Vavuniya.
The government was preparing to ferry supplies to the northern enclave under siege, as the convoy was stopped, aid workers said.
The UN says 160,000 people have been displaced in Sri Lanka's northeast and dozens have been confirmed killed during three weeks of fighting that has shattered hopes of sealing an end to years of ethnic strife soon.
The Tigers are furious at the Sri Lankan president's refusal to consider their demand for a separate ethnic homeland for minority Tamils in the north and east, and each side accuses the other of trying to start a full-blown war.
However, there was a relative lull in fighting on Sunday, with only sporadic exchanges of artillery fire in the northern Jaffna peninsula.
The military said it hoped a ship carrying 4,000 tonnes of food, aid and essentials would set sail for Jaffna - which is cut off from the rest of the island by Tiger territory and where food supplies are running out fast - as early as Monday.
Many foreign passport holders in Jaffna - most of them expatriate Tamils - are scrambling to register for any eventual evacuation, and are appealing to be ferried out on the ship bringing aid once the aid has been offloaded.