The Zambia Football Association forwarded to FIFA an investigation into allegations of sexual abuse, which The Guardian claimed this month that the coach was among the accused.
Mwape has denied the allegations and was asked if he had any intention of resigning from his role.
“What environment, affecting the team, in particular? What are you talking about?" he said in response.
“I would like to know, because there is no way I can retire [resign] without reason. Maybe your reason is because of what you are reading from the media, or from the press, but the truth of the matter should actually come out, not just rumours."
The manager was asked further questions about the matter, but a FIFA moderator interrupted to ask journalists to stick to questions about football and the tournament.
The press conference then ended prematurely.