Meriam Ibrahim, whose father was Muslim but whose mother was an Orthodox Christian from Ethiopia, was convicted of apostasy by a court in Khartoum in mid-May for marrying a Christian.
In a joint statement, the Sudanese churches said the charges against Ibrahim are false. They appealed to the Sudanese government to free her from prison, according to the social communications department of AMECEA, the Association of Member Episcopal Conferences in Eastern Africa, based in Nairobi, Kenya.
Rights groups and Western governments have also condemned the sentencing of 27-year-old Ibrahim, who is eight months pregnant.
Sudan's penal code criminalizes the conversion of Muslims to other religions, which is punishable by death.
AMECEA's May 23 statement said Ibrahim's husband, Daniel Wani, a U.S. citizen living in New Hampshire, claims that she is Catholic, but the association could not confirm this.
Sudanese officials will not allow Wani to take custody of his one-year-old son, who is with Ibrahim in prison, because, by law, a Christian man cannot raise a Muslim child.
In a May 23 letter to Sudanese President Omar al-Bashir, the World Council of Churches called the ruling an "egregiously unjust punishment" that violates the fundamental principle of international human rights law "embodied in Sudan's own constitutional guarantees to all of its citizens."
The Sudanese court also convicted Ibrahim of adultery for her 2011 marriage to Wani and sentenced her to 100 lashes. She has reportedly been held in prison for more than three months.