Former HP chief executive turned White House hopeful Carly Fiorina is waging a public relations war with CNN and the GOP establishment over her likely exclusion from the second Republican presidential debate next month, the New York Times reported.

During the first encounter of the party's candidates, hosted by Fox News, Fiorina was relegated to the afternoon debate of underdogs, while the top White House hopefuls faced each other in the evening, the newspaper recalled.

CNN similarly plans to determine the right to participate in its Sept. 16 event based on an average of public polls dating to mid-July.

But because the businesswoman performed well in the first debate and has since seen a steady rise in the polls, she is unhappy that the news network's formula includes surveys taken before that first encounter - a decision that will make it harder for her to earn a spot on the stage.

"We don't have national primaries, we have statewide primaries, and there are loads of state polls now,. They all say the same thing: I'm in the top five," Fiorina argued on Wednesday on MSNBC's "Morning Joe," CNN noted.

"I didn't think the Fox News rules were particularly good using national polls, (and) I don't think the CNN rules are particularly good - especially since they go all the way back to mid-July," she added.

But CNN countered that the rules for the debate had been agreed upon early on, in consultations with the Republican National Committee (RNC), and that its approach was "fair and effective."

"CNN published the criteria for the CNN-Reagan Library debate on May 20," the news channel said in a statement. "It will encompass polling data from three weeks prior to the first debate and five weeks following. Federal Election Commission guidelines make it clear that these criteria cannot be changed after they have been published."

Nevertheless, Fiorina suggested their steadfastness reflected negatively on both the channel and her party. "Let's forget that I'm a woman," she said. "I'm in ... the top 10 in national polls. So what does that say about CNN and the RNC?"