Christian Solidarity Worldwide says authorities will destroy churches in the Abel Santa Maria neighbourhood in the city of Santiago de Cuba.
Revd Alain Toledano, who leads one of the targeted churches, says that the authorities have also instructed pastors and families who live on the affected church properties are evicted.
The order, issued in late November, by government Planning and Housing Officials, came two weeks after members of the Emanuel Church, affiliated with the Apostolic Movement and led by Revd Toledano, started a "sleep in" to try to block government efforts to confiscate the property and destroy the church.
He told CSW that two churches affiliated with the Baptist and Assemblies of God denominations in Santiago, as well as two Assemblies of God churches in the Las Tunas Province, are under threat of government confiscation and demolition.
All churches in Cuba must be approved and registered by the state.
Kiri Kankhwende told Premier's News Hour that: "It's really fear - not just of the gospel - but of places where people gather together in places where the government fears they won't have control.
"The communist government likes to control ever facet of life - including church."
Revd Alain Toledano said: "There is a witch hunt against churches in Cuba at this time, mainly against the churches of apostolic and prophetic ministry.
"The communists have intensified in their hatred and persecution of the church following the Pope's visit to Cuba and the re-establishment of relations with the United States.
"I request constant intercession on behalf of the churches in Cuba. In our case, this would be the second time that the racist communists have attempted to evict us from our house, throw us out on the street and demolish our temple, only now their diabolical hatred and fury is directed at other congregations too."
Despite Revd Toledano having the correct paperwork showing their have government approval to carry out all the construction and renovation work which has taken place on the church, CSW said that the Cuban government has refused to register the Apostolic Movement.
He also said that one of the Assemblies of God churches under threat in Las Tunas is also facing demolition, despite the fact that the denomination is legally registered and the government issued permits for construction.
The threats against the churches appear to be part of a more general crackdown on religion, linked to new legislation that was passed in January.
The law, Legal Decree 322, gives more powers to the authorities to confiscate property.
CSW told Premier that some religious groups have been given the option to remain in the properties as tenants on the condition that they pay artificially high rent to the government and submit all their activities in advance to the Communist Party for approval, but most have rejected this.
CSW's Chief Executive Mervyn Thomas said: "We continue to call on the Cuban government to cease its harassment and persecution of religious groups across Cuba.
"The land grabs and attempts to manipulate religious organizations, linked to efforts to confiscate church properties, must end.
"It is clear that freedom of religion or belief has seriously deteriorated in Cuba over the course of the year since Legal Decree 322 came into force in January.
"We urge the European Union, the United States and other members of the international community to raise concerns about this law and its impact on freedom of religion or belief with the Cuban government as a matter of urgency, as well as the cases of these churches, which are currently under threat."
Listen to Premier's Antony Bushfield speak to Kiri Kankhwende from CSW here: