In a Declaration titled "Fiducia Supplicans: On the Pastoral Meaning of Blessings" (full text) issued by the Vatican's Dicastery for the Doctrine of the Faith and approved by Pope Francis, the Pope has given priests permission to give a blessing to same-sex or other unmarried couples. The Declaration says in part:
31. Within the horizon outlined here appears the possibility of blessings for couples in irregular situations and for couples of the same sex, the form of which should not be fixed ritually by ecclesial authorities to avoid producing confusion with the blessing proper to the Sacrament of Marriage. In such cases, a blessing may be imparted that ... descends from God upon those who—recognizing themselves to be destitute and in need of his help—do not claim a legitimation of their own status, but who beg that all that is true, good, and humanly valid in their lives and their relationships be enriched, healed, and elevated by the presence of the Holy Spirit. These forms of blessing express a supplication that God may grant those aids that come from the impulses of his Spirit ... so that human relationships may mature and grow in fidelity to the Gospel, that they may be freed from their imperfections and frailties, and that they may express themselves in the ever-increasing dimension of the divine love.
32. Indeed, the grace of God works in the lives of those who do not claim to be righteous but who acknowledge themselves humbly as sinners, like everyone else. This grace can orient everything according to the mysterious and unpredictable designs of God. Therefore ... the Church welcomes all who approach God with humble hearts, accompanying them with those spiritual aids that enable everyone to understand and realize God’s will fully in their existence.
Catholic News Service reported on the document, and summarized it as follows:
The Vatican offered a narrow set of conditions under which a priest or deacon could give a blessing to a same-sex or other unmarried couple, making it clear the church does not consider their unions a marriage but also recognizing how anyone can ask for a blessing when they are seeking God's assistance, mercy and grace.