Nelson Mandela's home town of Qunu.
A South African Press Association correspondent reported on Sunday night that police said they were investigating the incident.
"I now understand that this was not only about pictures [taken outside the Qunu home] … the two churches went there in groups. They were along the N2 road facing the gate and were not inside the homestead," said spokesperson Lieutenant Colonel Mzukisi Fatyela.
The groups were turned away from former president Mandela's Eastern Cape home on Sunday when they came to offer their prayers and support.
When the missionaries from the Reformed Church of Christ and the Apostolic Faith Mission arrived at the Mandela house, two police officers at the gate turned them away.
Two members of the group, while attempting to take pictures of themselves outside the house, were temporarily arrested and held inside a security room at the gate. This resulted in a heated exchange between the group and the police.
One police officer accused the group of betraying the freedom Mandela fought for.
Fatyela said he had inquired from a local police commander on what happened.
Mandela's house was open to villagers
"At first he [commander] down played the incident as a minor dispute about taking pictures, and after getting numerous inquiries from the media, new facts have come to light and I intend to meet the police commander and officers who were on duty to give statements on what occurred."
One of Mandela's grandson, Ndaba Mandela, told Sapa that he was shocked to hear about the incident.
"It is news to me, why would police clash with church members at home, it does not make sense," he said.
An elderly Mandela family member in Qunu, Silumko Mandela (67), said that it was known in the village Mandela's house was open to villagers.
"When we have any celebrations, villagers come and go there [Mandela's Qunu home] … I am surprised to hear about what occurred today," he said.
Apostolic Faith Mission women's leader Nomzingisi Jonga (44), who was present when the incident took place, said they were near the N2 road facing Mandela's home.
"We came here because we had a prophecy at our night vigil yesterday [Saturday], to pray for Madiba at his home. Now we were denied access and told not to pray in front of his gate." – Sapa