South Africa's Archbishop made his call in a pre-recorded message given to a conference held in Norway on the Rohingya.
"2015 is a big year for Myanmar with both a referendum on its constitution and a general election," Tutu said. "We have a responsibility to ensure that the plight of the Rohingya is not lost."
"We have a responsibility to persuade our international and regional aid and grant-making institutions, including the European Union, to adopt a common position making funding the development of Myanmar conditional on the restoration of citizenship, nationality, and basic human rights to the Rohingya," he said.
The 1984 Nobel laureate is an anti-apartheid hero respected around the world as a moral authority. Tens of thousands of Myanmar's 1.3 million Rohingya have fled the country in recent years, to escape sectarian violence as well as suffocating restrictions preventing travel and employment.
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Each year thousands of Rohingya try to flee Myanmar by boat headed for other Southeast Asian countries, spurring a human trafficking trade in often dramatic conditions.