(CNN) -

A Sudanese Christian woman who was sentenced to die for refusing to renounce her faith -- and then released -- was detained with her family on Tuesday as they tried to leave the African country.

Her legal team told CNN that Mariam Yehya Ibrahim, her American husband, Daniel Wani, and their two children were stopped at an airport in Khartoum and interrogated at national security headquarters in the Sudanese capital.

The problem involved what the legal team described as an alleged "irregularity with her documentation," according to Ibrahim's lawyers, who said she was in police custody.

Ibrahim has a U.S. visa and was headed to the United States with her family, her legal team said. The U.S. State Department said the family was stopped at the airport.

"The State Department has been informed by the Sudanese government that the family was temporarily detained at the airport for several hours by the government for questioning over issues related to their travel, and I think travel documents," said spokeswoman Marie Harf. "They have not been arrested. The government has assured us of their safety."

Harf said that the U.S. Embassy "has been and will remain highly involved in working with the family and the government," saying "we are engaging directly with Sudanese officials to secure their safe and swift departure from Sudan."

Sudanese authorities said Ibrahim had been detained because of the documents she submitted.

Sudan's National Intelligence and Security Services said that she had South Sudanese travel documents, despite not being a citizen of South Sudan, and she was heading to the United States, which is not her native country.

"This was considered illegal by the Sudanese authorities, who have summoned both the U.S. and South Sudanese ambassadors," the agency said in a message posted on its media Facebook page early Wednesday.

The airport detention came a day after Ibrahim's legal team announced the 27-year-old woman had been released from prison after weeks of international controversy over her conviction on apostasy and adultery charges.

According to her lawyer, the case began when one of Ibrahim's relatives, a Muslim, filed a criminal complaint saying her family was shocked to find out she had married Wani, a Christian, after she was missing for several years.

The Sudanese court considered Ibrahim a Muslim because her father was Muslim, but she said she was a Christian and never practiced Islam. She was charged with adultery, because a Muslim woman's marriage to a Christian man is illegal in Sudan, and with apostasy, accused of illegally renouncing what was alleged to be her original faith.

Authorities warned her to renounce Christianity by May 15, but she did not, instead responding that her mother, an Ethiopian Orthodox Christian, raised her as a Christian. She said her Sudanese Muslim father abandoned her when she was 6.

"I am a Christian," she said during her sentencing hearing last month, "and I will remain a Christian."

She was convicted and sentenced to death by hanging, along with 100 lashes. Sudanese Parliament speaker Fatih Izz Al-Deen defended the apostasy conviction, insisting last month that Ibrahim was raised in a Muslim environment.

After her sentence drew international condemnation from rights groups and foreign embassies in Khartoum -- including those of the United States, United Kingdom and Canada -- an appeals court this month ruled that the judgment against her was faulty and she was released, according to her lawyer.

Her husband, Wani, called CNN on Tuesday to say he and his family were being held at the national security office, but he provided no additional information. Ibrahim's legal team said the family was trying to leave the country when it was stopped by authorities and taken to the security headquarters.

Meanwhile, a man who says he is Ibrahim's brother, Al-Samani Al-Hadi, slammed the appellate court's decision and hinted at retribution.

"The family is unconvinced by the court's decision. We were not informed by the court that she was to be released; this came as a surprise to us," al-Hadi said Tuesday. "The law has failed to uphold our rights. This is now an issue of honor. The Christians have tarnished our honor, and we will know how to avenge it."

Al-Hadi did not comment on Ibrahim's detention at the airport on Tuesday. In court proceedings earlier this year, Ibrahim denied being related to al-Hadi.

Ibrahim gave birth to her second child -- a girl -- in prison last month. Her first child, a 1-year-old son, stayed with her at the prison but was free to leave at any time, Ibrahim's lawyer said.