Meriam Ibrahim and her family have taken refuge at the US embassy in the Sudanese capital of Khartoum following her release on bail.
The Christian Sudanese woman was detained until Thursday by the authorities after being charged with forgery and provision of false documents.
The Sudanese authorities charged Ibrahim after arresting her at the airport as she and her family attempted to leave the country for the US on Monday.
Her detention came just hours after being freed from prison following a judge's decision to drop apostasy and adultery charges against her.
Ibrahim was sentenced to death for apostasy on May 11 because the state deemed her marriage to a Christian man, Daniel Wani, to be void.
While Ibrahim testified to being a lifelong Christian, the state refused to recognise her faith and insisted she was a Muslim because this was her father's faith.
Wani, a US citizen, told Agence France-Presse that the family has now sought refuge from the US embassy because of death threats against his wife.
The Guardian reports that she was released from police custody on the condition that she remains in Sudan.
Asked by the BBC about her plans following her release on Thursday, Ibrahim said: "I will leave it to God. I didn't even have a chance to see my family after I got out of prison."