The White House has not clarified what the stay-behind mission will entail, nor how long it will last.
Haley outlined her agenda for the United Nations, including human rights and peacekeeping reform.
Many of Haiti's people are without drinking water and the spread of cholera is all but certain.
Ban's prepared speech appeared to praise Russia's role in "ending conflicts in Ukraine and Syria."
Beijing currently has 3,000 troops on peacekeeping duty; the U.S. has less than 100.
Human Rights Watch called on Sudan's government to disband the Rapid Support Forces.
A new campaign urges the United Nations to strip peacekeepers of their immunity from prosecution.
Israel received the message a day after the worst deadly clashes in years erupted along the border.