A Sudanese woman sentenced to death for refusing to recant her Christian faith after allegedly converting from Islam has appealed against the sentence, her lawyer said.

The appeal demands the release of Meriam Ibrahim, saying the court that tried her committed "procedural errors", according to her lawyer Eman Abdul-Rahim.

Ms Ibrahim was sentenced to death for apostasy last month by a Khartoum court for allegedly converting to Christianity from Islam. She maintains that her Muslim father left when she was young and that she was raised a Christian by her Ethiopian mother, who is an Orthodox Christian.

Ms Ibrahim married a Christian man from southern Sudan in a church ceremony in 2011. As in many Islamic nations, Muslim women in Sudan are prohibited from marrying non-Muslims, although Muslim men can marry outside their faith.

She has a son, 18-month-old Martin, who is living with her in jail, where she gave birth to a second child last week. By law, children must follow their father's religion.

Amnesty International condemned the sentence, calling it "abhorrent", and the US State Department said it was "deeply disturbed" by the case.

Sudan introduced Islamic shariah law in the early 1980s under the rule of autocrat Jaafar Nimeiri, a move that contributed to the resumption of an insurgency in the mostly animist and Christian south of Sudan.

The south seceded in 2011 to become the world's newest nation, South Sudan.

Sudanese president Omar Bashir, an Islamist who seized power in a 1989 military coup, has said his country will implement Islam more strictly now the non-Muslim south is gone.

A number of Sudanese have been convicted of apostasy in recent years, but they all escaped execution by recanting their new faith.

Religious thinker and politician Mahmoud Mohammed Taha, a critic of Mr Nimeiri and his interpretation of shariah, was sentenced to death for apostasy. He was executed in 1985 at the age of 76.