Mrs. Clinton anticipated the sensitivity of the issue for some more conservative countries, saying that “the obstacles standing in the way of protecting the human rights” of lesbians, gay men, bisexuals and transgendered people “rest on deeply held personal, political, cultural and religious beliefs.”

She argued that gay rights transcended national, political and even culture boundaries, casting them as universal rights like those adopted by 48 nations in the aftermath of World War II in what was called the Universal Declaration of Human Rights.

Mrs. Clinton’s aides so worried about the reaction of some countries at the Human Rights Council that they did not advertise the theme of her remarks before she delivered them. In the end, no representatives from the council’s 47 member nations walked out, and the audience gave her a standing ovation.

The administration’s announcement formalizes several steps that Mrs. Clinton has already ordered. She has asked American diplomats to raise the issue wherever harassment or abuse arises and required a record of them in the State Department’s annual report on human rights. On Tuesday, she also announced a $3 million program to finance gay-rights organizations to combat discrimination, violence and other abuses.

A senior administration official said that the money could be used, for example, to finance a lawyers’ group that is defending gays or to pay for the training of journalists who cover the persecution of gays. It could also provide relocation aid to refugees fleeing violence or persecution.

“I am deeply concerned by the violence and discrimination targeting L.G.B.T. persons around the world,” Mr. Obama said in the memorandum, referring to lesbian, gay, bisexual and transgender people, “whether it is passing laws that criminalize L.G.B.T. status, beating citizens simply for joining peaceful L.G.B.T. pride celebrations, or killing men, women and children for their perceived sexual orientation.”

He said in the memorandum that the State Department would lead other federal agencies to help ensure that the government provided a “swift and meaningful response to serious incidents that threaten the human rights” of gay, lesbian, bisexual and transgender people abroad.