"The World Bank is deeply concerned with the economic and development impact of the unresolved oil issues and how this will affect the people of both South Sudan and Sudan, particularly the most vulnerable," it said in a statement.
Offering support to both Juba and Khartoum to ensure the "protection of vulnerable people from economic hardship," the Bank said the rivals were struggling after a furious dispute over oil payments.
"Given the desperate living situation being faced by people in both Sudan and South Sudan, the World Bank's economic analysis unambiguously shows that it is in the interests of both countries to resume talks urgently," the Bank added.
South Sudan broke away from Sudan in July after a 2005 peace deal ended one of Africa's longest civil wars, which killed about two million people.
But tensions soon flared again over a series of unresolved issues, including the border, the future of disputed territories and oil.
As a result of independence, landlocked South Sudan took with it about 75 per cent of the formerly united Sudan's oil production, worth billions of dollars.
In a key dispute, the two sides were unable to agree on how much the South should pay to export its crude through a northern pipeline and port, leading the Juba government in January to shut its production after Khartoum began seizing the oil in lieu of payment.
The poverty-stricken South said 98 per cent of its pre-shutdown revenue came from oil.
A border war with South Sudan began in late March, escalating with waves of Sudanese air strikes against South Sudanese territory and the South's 10-day seizure of the Heglig oil field from Khartoum's army.
Both sides say they are complying with a United Nations Security Council resolution which ordered them to stop fighting from last Friday.