The former Cardiff boss has admitted sending three "completely unacceptable" texts.
But on Saturday the Daily Mail published details of four further messages. One of those, it is claimed by the newspaper, makes a racist reference to Cardiff's Malaysian owner Vincent Tan. The other three are of a sexist and homophobic nature, it is alleged.
In an interview on Friday night on Sky Sports News HQ, Mackay denied being racist, sexist and homophobic.
"Out of 10,000 text messages in and out of someone's phone I sent three and that being the case, looking at them they are completely unacceptable, inappropriate and for that and for any offence I've caused I sincerely apologise for that," Mackay said.