Meriam Ibrahim, the Christian woman released from death row in Sudan on Monday, was detained with her husband and two children at Khartoum airport on Tuesday as the family attempted to leave the country.

Agents from the National Intelligence and Security Services (Niss) apprehended the family just 24 hours after Ibrahim was released on the orders of the appeal court.

Her lawyer, Elshareef Mohammed, who was with Ibrahim at Khartoum airport at the time, said more than 40 security officers prevented the family from boarding a plane to the US. Ibrahim's husband, Daniel Wani, is a US citizen.

"It's very disappointing," Elshareef said. "They were very angry. They took us [the family's lawyers] outside, and took the family to a Niss detention centre. They have not been given access to lawyers."

Meriam Ibrahim holding her daughter Maya, who was born in prison. Her husband Daniel Wani sits to her right holding their son Martin Photograph: theguardian.com

He said the appeal court had quashed Ibrahim's convictions and there were no restrictions on her travelling. He added that political differences within the government over the case may have played a part in the decision to prevent her leaving. "I'm very concerned. When people do not respect the court, they might do anything."

On Tuesday night, news agencies in Khartoum said Ibrahim had been transferred from Niss custody to a police station, where she was being questioned about her documents.

A Sudanese source told Agence France-Presse that Ibrahim was under investigation but had not been charged, and that her husband and children were with her but were not suspected of wrongdoing.

In Washington, state department spokeswoman Marie Harf said the family had been "temporarily detained for several hours over questions related to their documents". She added: "They have not been arrested. The government has assured us of their safety. The embassy has and will remain highly involved in working with the family and the government."

The detention came a few hours after photographs were released by Ibrahim's lawyers showing the family reunited after her four-month incarceration, during which she gave birth to the couple's daughter while shackled to the floor of her prison cell. Her 21-month-old son, Martin, was kept in Omdurman prison with her. The photographs showed Ibrahim holding two-week-old Maya, seated next to Wani, who uses a wheelchair due to muscular dystrophy. Martin is sitting between his knees.

Ibrahim, 27, had been sentenced to death for apostasy. She insisted that she had been brought up as a Christian, despite her father being Muslim. She was also sentenced to be publicly flogged for adultery following a court's ruling that her marriage to a Christian man was invalid.

After her release, Wani said he hoped the family would be able to start a new life in the US. Ibrahim, Wani and their two children were taken to a safe house following her release from prison amid fears for the family's safety. Men claiming to be Ibrahim's relatives, whose allegations against her triggered the court case, had threatened to carry out the death sentence if she was released from prison. Ibrahim denied knowing them.

Wani has claimed that those who had triggered the case against his wife were trying to get their hands on her business interests, which include a hair salon, mini-mart and agricultural land.

Mashood Adebayo Baderin, a UN independent expert on human rights in Sudan, told a press conference in Khartoum before news of the family's detention broke that if Ibrahim had received death threats, "as a citizen of this country, Sudan has a duty to protect its citizens".

The case "raises important legal questions about the right to freedom of religion and belief", he added.

Amnesty International said it was investigating reports of the family's detention. Ibrahim's supporters expressed outrage at her arrest on Twitter, with some demanding President Obama intervene with a personal appeal to the Sudanese government to release the family. Others called for prayers.

Ibrahim's case has attracted international criticism. More than 1 million people have backed a campaign by Amnesty International to free her.

Ibrahim was convicted of apostasy after the court insisted she was a Muslim because her father was a Muslim, even though Ibrahim said she had been brought up as a Christian after her father abandoned the family when she was six. Under the Sudanese penal code, Muslims are forbidden from changing faith, and Muslim women are not permitted to marry Christian men.

Following her conviction last month, she was given three days to renounce her faith or face a death sentence. She refused to recant, telling the court: "I am a Christian and I am not an apostate."

Then eight months' pregnant, she was told her death sentence would be deferred for two years to allow her to nurse her unborn baby.

Wani claimed that the US embassy in Khartoum had dismissed his requests for help as a US citizen after his wife was jailed. A state department spokesperson said officials in the Sudanese capital had been in regular contact to offer assistance to Wani.

In a separate move, the Sudanese authorities shut down a 17-year-old centre for women's rights without explanation yesterday, according to Agence France Presse.