• Responding to a group of cardinals who asked him for clarity on the issue, he said any request for a blessing should be treated with "pastoral charity".
• He added, however, that the Church still considered same-sex relationships "objectively sinful" and would not recognise same-sex marriage.
Pope Francis has suggested he would be open to having the Catholic Church bless same-sex couples.
Responding to a group of cardinals who asked him for clarity on the issue, he said any request for a blessing should be treated with "pastoral charity".
"We cannot be judges who only deny, reject, and exclude," he said.
He added, however, that the Church still considered same-sex relationships "objectively sinful" and would not recognise same-sex marriage.
The request was one of a number sent to the Pope ahead of a weeks-long global gathering to discuss the future of the Church set to get under way at the Vatican on Wednesday.
In the Catholic Church, a blessing is a prayer or plea, usually delivered by a minister, asking that God look favourably on the person or people being blessed.
Bishops in a number of countries, including Belgium and Germany, have begun to allow priests to bless same-sex couples, but the position of Church authorities remained unclear.
In 2021, following a similar request for clarification, the Vatican's doctrinal office ruled against allowing the practice.
Responding to the latest request, the Pope said that the Church understood marriage to be an "exclusive, stable, and indissoluble union between a man and a woman" and should avoid "any type of rite or sacramental that might contradict this conviction".
But he added that "when a blessing is requested, it is expressing a plea to God for help, a supplication to live better".
"Pastoral prudence must adequately discern whether there are forms of blessing, requested by one or more persons, that do not convey a mistaken concept of marriage," he said.
Appearing to suggest that requests for blessings should be considered on a case-by-case basis, he said that "decisions that may be part of pastoral prudence in certain circumstances should not necessarily become a norm".
"Canon law should not and cannot cover everything," he said.
He added that the Church should always approach its relationships with people with "kindness, patience, understanding, tenderness, and encouragement".
In February, a vote of senior figures in the Church of England backed proposals to allow prayers of blessing for same-sex couples.
The move would mean a same-sex couple could go to an Anglican church after a legal marriage ceremony for services including prayers of dedication, thanksgiving, and God's blessing.