UNITED NATIONS  An unprecedented declaration seeking to decriminalize homosexuality won the support of 66 countries in the United Nations General Assembly on Thursday, but opponents criticized it as an attempt to legitimize pedophilia and other “deplorable acts.”

The United States refused to support the nonbinding measure, as did Russia, China, the Roman Catholic Church and members of the Organization of the Islamic Conference. The Holy See’s observer mission issued a statement saying that the declaration “challenges existing human rights norms.”

The declaration, sponsored by France with broad support in Europe and Latin America, condemned human rights violations based on homophobia, saying such measures run counter to the universal declaration of human rights.

“How can we tolerate the fact that people are stoned, hanged, decapitated and tortured only because of their sexual orientation?” said Rama Yade, the French state secretary for human rights, noting that homosexuality is banned in nearly 80 countries and subject to the death penalty in at least six.