The United Nations World Food Programme estimates that it may have lost more than 3,700 tonnes of food in looting in South Sudan.
WFP spokeswoman Elisabeth Byrs said the food was enough to feed 220,000 people for a month
WFP's warehouses in Malakal had been almost entirely emptied, she told a regular UN briefing in Geneva.
The agency was working to recover lost stocks wherever possible and trying to protect remaining stocks, she said.
Meanwhile, South Sudanese rebels accused the army of attacking their positions, claims the military denied, hours before a ceasefire deal agreed by government and rebels comes into effect.
A rebel spokesman said "simultaneous attacks have been launched" by the army on rebel positions in the northern oil state of Unity, and in the volatile eastern Jonglei region.
But army spokesman Philip Aguer said he had "no reports of fighting", and that clashes in Jonglei had taken place yesterday before the deal was signed, when rebels attacked government forces.