"This was an outrageous and cowardly attack against U.N. staff, which cannot be justified under any circumstances and I condemn it in the strongest possible terms," Ki-moon said from Kenya, where the United Nations said he is making an official visit.
Jones initially cancelled his plans for the book burning on the ninth anniversary of the Sept. 11 terror attacks. The stunt, according to Jones, was a protest against the Muslim-backed community center that was to be built near the site of the September 11 attacks in New York.
During that initial incident, Gainesville's mayor told reporters Jones does not speak for the community.
"He's a really fringy character," said Pegeen Hanrahan, a two-term mayor who left office in May. "For every one person in Gainesville who thinks this is a good idea there are a thousand who just think it's ridiculous."
"He's a person who has a congregation that's exceedingly small, maybe 30 or 40 people -- 50 on a good day," Jacki Levine, managing editor of the Gainesville Sun newspaper, said in September. "He is not at all reflective of community he finds himself in."
ABC News' Lauren Effron and The Associated Press contributed to this report.