Gay couples may get blessed in British churches
The church said priests may "devise accommodations" for such same-sex couples, the Daily Mail reported.
It said public prayers which recognise gay relationships could be introduced in church services by "sympathetic" clergy.
Backed by Archbishop of Canterbury Justin Welby and leading bishops, the statement, however, does not change the church's laws which say homosexual activity is "sinful" and ban priests from blessing gay relationships, the daily said.
But it appeared to encourage same-sex couples, saying the church must show "flexibility" over gay relationships.
The statement came at a time of conflict between the church and the government over same-sex marriage.
Laws permitting men to marry men and women to marry women are likely to be passed within a few months.
The church, along with other major faith organisations, has protested that the government has no power to change the principle that marriage must be between a man and a woman.
The church has warned that the new law could lead to disestablishment, the severing of the 480-year-old link between the church and the state.
The Bishop of Coventry the Right Reverend Christopher Cocksworth said the statement did not mean that churches could stage public services of blessing for gay couples, which are banned by church law.
He said that priests might offer such couples "attention, care and prayer".
But campaigners for gay rights said it meant a green light for clergy who wish to give public recognition to gay relationships.