Eritrean government officials asked health centre administrators to sign a document approving the handover.
However, most of the administrators refused to sign and told the officials to talk to the church leaders.
Security officers then removed the staff from the health centres and closed them down. It is not yet known why the Eritrean government took this action.
It's part of a wider disagreement between Christians and the Eritrean government.
In April, Eritrean Catholic bishops called for a national reconciliation process that ensures justice for everyone. In the wake of the peace deal signed with Ethiopia, Eritrean bishops wrote a 30 page letter saying that the nation should come together and heal.
They called on the government to make reforms that would stop people wanting to leave the country.
The closure of the health centres also follows the arrest of 30 underground Christians in Eritrea at the beginning of June who were members of a Pentecostal church, an unregistered and therefore illegal denomination.
According to reports, police arrested the Christians while they were gathered at three different places in the capital Asmara.
A further 141 Christians were arrested in May and police regularly raid the homes of Christians from unregistered denominations, often only being released if they renounce their faith.
Eritrean Christians who are not members of state approved churches are considered agents of the West and a threat to the state and the government only recognises three Christian denominations, including the Eritrean Orthodox Church.
Hundreds of Christians who are members of unregistered churches are in prison, some have been held captive for over a decade.
Many are forced to work long hours in commercial flower fields, and some are held in shipping containers in scorching temperatures, according to the charity Open Doors.
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