Meriam Ibrahim, who gave birth to a daughter in custody, will be freed in a few days, the official told the BBC.
Abdullahi Alzareg, an under-secretary at the foreign ministry, said Sudan guaranteed religious freedom and was committed to protecting the woman.
Khartoum has been facing international condemnation over the death sentence.
In an interview with The Times newspaper, British Prime Minister David Cameron described the ruling as “barbaric” and out of step with today’s world.
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