Rice added that she had urged Museveni to not sign the bill.
Former president Bill Clinton, who has worked on health initiatives in the country through his Clinton Foundation, said he was “strongly opposed to its move to criminalize homosexuality.”
“It is a setback for personal freedom and equal rights and a rebuke to Uganda’s own commitment to protecting the human rights of its people,” Clinton added.
“I want to salute and encourage the brave Ugandans committed to the fundamental dignity of all people and urge the government to reverse this decision.”
Museveni, a devout evangelical Christian, has expressed the view that gays are “sick” and “abnormal.”
He suggested in a letter to parliament that homosexuality was caused by a genetic flaw, or a need to make money.
Nevertheless, he refused to sign the anti-gay legislation last month.
“He does not approve of homosexuality but he believes that these people have a right to exist,” presidential spokesman Tamale Mirudi told AFP at the time, explaining why the bill had been rejected.
Homophobia is widespread in Uganda. Gay men and women face frequent harassment and threats of violence, and rights activists have reported cases of lesbians being subjected to “corrective” rapes.