Unknown assailants hacked to death to Xulhaz along with another inside a house in capital Dhaka’s Kalabagan on Monday.
Xulhaz was an employee of the US mission in Dhaka.
“We abhor this senseless act of violence,” the ambassador said in a statement.
“Xulhaz was more than a colleague to those of us fortunate to work with him at the US Embassy. He was a dear friend,” she said.
"Our prayers are with Xulhaz, the other victim, and those injured in the attack."
Reuters news agency reported that the Department of State said the United States was outraged by the "barbaric attack".
“We are outraged by the barbaric attack on Mr Xulhaz Mannan, a beloved member of our embassy family and a courageous advocate for LGBTI (lesbian, gay, bisexual, transgender and intersex) rights, human rights, actually," State Department spokesman John Kirby told reporters.
Kirby also said he did not know the motivation for the killing, adding that Xulhaz had done work for the US Agency for International Development.