".@CarlyFiorina had to inject herself into my factual statements concerning Ben Carson in order to breathe life into her failing campaign!," he tweeted.
Trump said on CNN's "Erin Burnett OutFront" Thursday that Ben Carson's self-described "pathological temper" is incurable -- adding that it's like the sickness of a "child molester."
Later that night, Fiorina chimed in to "interrupt" Trump -- a reference to a complaint Trump made about her at Tuesday's Republican debate.
"Donald, sorry, I've got to interrupt again. You would know something about pathological," Fiorina said in a Facebook post
. "How was that meeting with Putin? Or Wharton? Or your self funded campaign? Anyone can turn a multi-million dollar inheritance into more money, but all the money in the world won't make you as smart as Ben Carson."
Trump on Friday defended his attacks on Carson.
".@CarlyFiorina Ben Carson said in his own book that he has a pathological temper & pathological disease. I didn't say it, he did. Apology?," Trump tweeted.
Trump denied that he singled out Fiorina for interrupting other candidates.
".@CarlyFiorina Carly, not just you, I also told Gov. Kasich to "let Jeb talk, give him a chance" because Kasich was constantly cutting in," he tweeted.
And the Ivy League grad defended his academic pedigree.
".@CarlyFiorina Carly—I did graduate from Wharton and did very well. Who is your fact checker? Will you apologize?," he tweeted.
He also clarified the statement he made on the Fox Business Network debate about being on "60 Minutes" with Putin.
".@CarlyFiorina I only said I was on @60Minutes four weeks ago with Putin—never said I was in Green Room. Separate pieces—great ratings!," he tweeted.
This exchange was the latest in an ongoing tiff battle between Trump and Fiorina -- both political outsiders with extensive business experience seeking the Republican nomination.
Fiorina previously criticized Trump for making comments about her appearance
that she considered sexist, and Trump later said she had a beautiful face
. The two have attacked each other's business acumen with Trump pointing out her controversial tenure
leading Hewlett-Packard and Fiorina mentioning Trump's multiple business bankruptcies
. And Fiorina -- who often presents herself as a conservative alternative to Hillary Clinton -- often blasts Trump for his previous association
with the former secretary of state.