By Mike Lanchin
BBC News religious affairs correspondent
May 26, 2007
He said they should spend time on more pressing issues in the region.
Speaking to the BBC World Service, the South African bishop said Zimbabwe, HIV/Aids and the crisis in Darfur were not getting sufficient attention.
Zimbabwe's Anglican church also lacked courage to stand up to President Robert Mugabe's regime, he said.
This was the 76-year-old Nobel peace laureate touching raw nerves for the Anglican church in Africa on very sensitive subjects.
In his usual forthright manner, Archbishop Tutu told the BBC that the Anglican communion was spending too much of its time and energy on debating differences over gay priests and same sex marriages - a subject, he said, that had now become "an extraordinary obsession".
He said: "We've, it seems to me, been fiddling whilst as it were our Rome was burning. At a time when our continent has been groaning under the burden of HIV/Aids, of corruption.