Meriam Ibrahim freed from death row on Monday has been detained with her
family at Khartoum airport
Meriam Ibrahim was sentenced to hang in May for renouncing Islam, sparking widespread outrage at home and abroad. About 40 security agents detained Mrs Ibrahim - along with her husband, Daniel Wani and two children - at the airport,
On Monday, Mr Wani said the family intended to leave for the US.
Mrs Ibrahim was released from prison after an appeal court annulled the death sentence imposed on her.
She was arrested in February, and gave birth to a daughter in prison not long after being sentenced.
The family has been taken to the headquarters of one of Sudan's security agencies.
Before she was detained on Tuesday, Western countries had welcomed the decision to rescind the death penalty.
Analysis: James Copnall, former BBC Sudan correspondent
The National Intelligence and Security Service (NISS) is an extremely powerful body, which frequently intervenes in Sudanese politics.
It is a key part of the informal coalition - also comprising the military, Islamists and pragmatists - which rules Sudan.
The different components are constantly jockeying for a better position.
In recent times, NISS has been flexing its muscles.
It is very possible that NISS did not like the decision to release Meriam Ibrahim, and re-arresting her and her family was a way of making this point to the rest of the Sudanese government.
However, security is not a homogenous entity either.
It is also conceivable that one part of NISS accepted Mrs Ibrahim's release, while another section was not happy with it.
Mrs Ibrahim's release and re-arrest simply underlines the fact that there are many decision-makers in Sudanese politics, and they do not always agree with each other.
Sudan has a majority Muslim population, and Islamic law has been in force there since the 1980s.
Even though Mrs Ibrahim was brought up as an Orthodox Christian, the authorities considered her to be a Muslim because that is the religion of her father.
Mr Wani has US citizenship.
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