Teotihuacán is a popular tourist and archaeological site outside Mexico City; officials said they will maintain security in the area as they investigate the incident.
"Much about the times we now live in, I suspect, may have troubled her deeply," the king said of his late mother Queen Elizabeth II in a televised statement.
The return will be especially difficult for older residents of Wang Fuk Court, who made up over a third of the 4,600 people who lived there before the blaze that killed 168 people.
South Korean police have requested a detention warrant for the chairman of HYBE over alleged illegal trading tied to the company's initial public offering.