A traditional Ghana priest has sparked a national outcry after marrying a 13-year-old girl, prompting calls for his arrest.

The 63-year-old priest Nuumo Borketey Laweh Tsuru XXXIII, also known as Gborbu Wulomo, married the girl in a traditional ceremony on Saturday near the capital Accra.

The girl and her mother were placed under police protection soon after the marriage as Ghana's attorney general opened an investigation.

"The allegations, if proven, constitute a criminal offence for which all persons involved must face prosecution," a statement from the attorney general's office said.

Under Ghanaian law, the legal minimum age for marriage is 18.

Police and officials say the girl is 13, but the traditional authorities involved say she is 16.

Defending his actions, the priest's spokesperson insisted the marriage was not about sexual relations.

Without giving her age, he said the girl would not be expected to fulfil marital duties until she reaches the legal age of consent, which is 16 in Ghana.

"It's not a marriage ceremony. There is nothing sexual attached to it. The priest has three customary wives already. It's a customary role to help the priest with his spiritual duties," spokesperson Mankralo Shwonotalor told AFP by telephone.

He said her rights had not been infringed and the girl was still attending school.

But public condemnation intensified over the traditional ceremony.

Gender activist and former minister Nana Oye Bampoe Addo said the marriage was illegal.

"The state must act immediately," she told AFP, saying the cultural practice was incompatible with Ghana's law and constitution.

"What has just happened is a crime and unlawful."