The Athletic reported on Wednesday that a Filipino man said to be in his early 40s died while working at the base of Saudi Arabia during the group stage.
According to the report, the incident is being investigated by the Qatari government.
Asked by the BBC for a comment on the reports, Al Khater extraordinarily said "death is a natural part of life" as he questioned why the interviewer had chosen to ask him about the incident.
He said: "We're in the middle of a World Cup and we have a successful World Cup, and this is something you want to talk about right now?
"I mean, death is a natural part of life, whether it's at work or in your sleep.
"Of course, a worker died, our condolences go to his family, however this is strange this is something you want to focus on as your first question."
The Qatar World Cup has been dominated by off-field issues, such as the host nation's questionable human rights and its treatment of migrant workers.
On Thursday, FIFA secretary general Fatma Samoura was asked by Reuters for a comment on the incident.
"We've already elaborated... about what we are doing in Qatar," she said.
"We are talking about things we have already discussed for months and months, time and time again."
At the time of publication, FIFA had not responded to Stats Perform's request for comment.