Kenyan police say they have asked the British government to extradite the UK-based Kenyan evangelist, Gilbert Deya.
Children's charities fear a child-trafficking operation
The pastor claims infertile UK couples are able to conceive after prayer and denies allegations that the "miracle babies" are stolen from Kenya.
On Monday, five people were charged by Kenyan police with stealing babies, including Mr Deya's wife, Mary.
The court had heard that Mary Deya told the police that she had given birth to nine children in a miraculous way.
DNA tests carried out on the children seized from her Nairobi home, show only one belongs to the Deyas.
The court also heard that another woman, Eddah Odera, claimed to have had 11 babies between 1999 and June of this year.
Eleven children were also seized from her house and DNA tests ruled out any links to her and her husband, Michael.
Police say their investigations are now focused on Kenya's largest maternity hospital after 24 couples claimed their babies were stolen from the hospital immediately after birth.
Gilbert Deya Ministries say they are expanding fast
Most say they were informed by the hospital authorities that their child had died shortly after birth.
A former nurse at Nairobi's Pumwani maternity hospital has also been arrested.
The children, some only a few weeks old, are in protective custody.
Both the Church of England and the Royal College of Obstetrics and Gynaecology have urged the Metropolitan Police to investigate claims involving members of the Gilbert Deya Ministries.
The church has 36,000 members in the UK, as well as branches in Europe, Africa and Asia.
Kenyan Prosecutor Moses Odoyo told the court the investigation involved suspects in Britain, Ghana, Nigeria and Uganda, as well as Kenya.
All five defendants in Kenya have denied stealing babies and have been released on bail, due back in court on 3 November.