The Republican claimed she showed "bias" for mentioning the groping allegations against Donald Trump.
Ms Kelly retorted she was not fascinated by sex but by who was going to be in the White House.
The Fox News journalist has previously angered Mr Trump for questioning his attitude towards women.
Mr Trump publicly criticised Ms Kelly on a number of occasions after she asked about derogatory remarks he had made - including calling women "fat pigs" - during the Republican primaries in 2015.
