The study by the United Nations called on the security council to refer the situation to the International Criminal Court.
Aid to the Church in Need said it had "demanded the UK Government take action to address the situation".
The UN report said it found evidence of human rights violations, including killings, torture, rape and sexual slavery, forced religious conversions and the conscription of children.
"It is reasonable to conclude that some of these incidents, considering the overall information, may constitute genocide," the report states.
Neville Kyrke-Smith, National Director Aid to the Church in Need (UK), said: "Aid to the Church in Need very much welcomes the report by the office of the United Nations High Commissioner for Human Rights.
"In the UK we are fortunate to have the freedom to live out our faith, but the terrible reality is that Christians and other religious minorities in Iraq do not.
"We therefore call on our Prime Minister (David Cameron) and the leaders of every political party to take action to support the religious minorities of Iraq and for the human right of religious freedom to be upheld around the world."