Christian Solidarity Worldwide (CSW), which promotes religious freedom, has been calling upon the US President to raise the matter of Revd Alain Toledano's treatment, during a visit to Cuba next month.
The organisation said last month the scale of persecution being encountered by Christians in Cuba is unlike anything seen before.
Police apparently told Revd Toledano charges are being prepared against him concerning the alleged illegal possession of chairs and supports for the roof of his now-destroyed Emanuel Church in the east of the country.
Picture: Havana, Cuba's capital city.
In a meeting with government officials and the police chief yesterday, Revd Toledano was reportedly informed that a criminal case against him would be referred to the Revolutionary Tribunal.
Revd Toledano is part of the Apostolic Movement, a network of churches CSW claims the Cuban government has refused to register.
BREAKING NEWS: Reverend Alain Toledano of Emanuel Church, #Cuba, has been threatened with arrest. Read more: https://t.co/8c1PEAVo0z
— CSW_UK (@CSW_UK) February 24, 2016
He is said to have been out of the country when his home and church were demolished. However, six state security agents reportedly visited him on his return, warning him not to hold religious meetings or go out into the street.
Revd Toledano claims the demolishing of his church on February 5 and the dragging of his wife out of bed during the incident has left his family exhibiting signs of emotional trauma.
He said: "My daughters toss and turn all night and during the day they are dazed and fearful."
Picture: Ariel view of Havana.
CSW's Chief Executive Mervyn Thomas said: "We are deeply concerned for the welfare of Reverend Toledano and his family, whose only 'crime' has been to lead a peaceful, growing church.
"We call on the United States and the European Union to raise this case urgently with the Cuban government, urging it to cease its harassment of this family and their church.
"We also urge President Obama to condemn the serious deterioration in religious freedom in Cuba when he visits the island in March and to continue to press for improvements in respect for human rights."