The assembly will take up the document, called "Discrimination on the Basis of Sexual Orientation and Gender Identity," in its next session in April.
The delay was caused by "the large number of amendments opposing the report," according to the European Center for Law and Justice.
A statement from that group explained the document "faced today a very strong opposition mainly because it notably diminishes and even threatens fundamental rights, such as the freedom of speech, the freedom of religion and conscience, the higher interest of children and the states’ sovereign interest and right to protect public morality, family and the best interests of the child."
Grégor Puppinck, director of the European Center for Law and Justice, told ZENIT that the resolution "tends toward forcing opinions and consciences, imposing the idea that every type of relations -- heterosexual, homosexual, bisexual or transexual -- would be equal from the point of view of nature and morality."
Puppinck explained the erroneous philosophy underlying the resolution: "Human sexuality, like every voluntary activity, has a moral dimension: It is an activity that involves the individual will at the service of an end; it is not an 'identity.'
"In other words, it pertains to act and not to being, even if homosexual tendencies could be profoundly rooted in the personality."
He noted that sexual activity is being compared to elements such as race, age or being male or female. But, he clarified, these latter criteria pertain to "being," not act.
When sexuality is removed from the sphere of morality, Puppinck added, the "moral justification for a difference in treatment -- for a discrimination -- is made impossible: the distinct types of sexual behavior are presented in the abstract as neutral and equivalent among themselves."
"Expressing an opinion on the matter is made impossible and even prohibited," he noted.
The center is also opposing another measure before the assembly: A vote is expected Friday on a strategy for population reduction, which will promote abortion.