The organisation's research has shown in 2014 there were 230 violations of religious freedom documented, up from 185 the year before.
CSW claimed all religious groups have been targeted, but said the majority of the violations were against Roman Catholic human rights defenders and pro-democracy activists.
It reported some people were stopped from participating in religious activities, and had on occasions violently been stopped, by state security and police.
CSW asked the USA to raise two issues with the Cuban government: the release of Revd Jesús Noel Carballeda, who has been held without charge in a Cuban prison since February and the legalisation of all unregistered groups.
In Cuba religious groups must be approved by the government before operating in the community. CSW has asked the Cuban authorities to respect the right of everybody to practice and respect property belonging to religious groups.
Chief Executive of CSW, Mervyn Thomas said: "We urge the United States to include respect for freedom of religion or belief for all as a key part of these dialogues and to press the Cuban government for a commitment to improving its record in this area.
"While a few religious groups in Cuba have received special privileges in the past few years, including permission to build a handful of new churches, these rights have not been extended to all religious groups and thus cannot be considered an improvement in respect for freedom of religion or belief.
"The Cuban government must be held to account for its continued violations of this right and should be urged to legalise all religious groups, release Revd Carballeda, allow all Cuban citizens to participate in religious activities without regard for their political beliefs, and to cease its threats to confiscate or destroy properties associated with registered and unregistered."