Donald TrumpDonald John TrumpO’Malley tells Dems not to fear Trump Right way and wrong way Five things to know about the elephant trophies controversy MORE blasted Sen. Ted CruzRafael (Ted) Edward CruzTexas Republicans slam White House over disaster relief request Dem rep: Trump disaster aid request is 'how you let America down again' Moore endorsements disappear from campaign website MORE (Texas) as the "single biggest liar" and a "nasty guy" as the two traded insults during Saturday's Republican presidential debate.

"You are the single biggest liar, you are probably worst than Jeb Bush," Trump said to Cruz, after the senator called him a liberal.

He bashed Cruz for his campaign spreading an ultimately false assertion that fellow candidate Ben Carson was dropping out on the day of the Iowa caucuses.

"This guy will say anything, nasty guy. Now I know why he doesn't have one endorsement from any of his colleagues," Trump added.

Cruz has endorsements from members of the House, but none from senators. 

The billionaire's comments came after Cruz accused him of being a liberal for most of his life and for supporting taxpayer funding for Planned Parenthood. 

He pushed back against Trump, noting that he has also made remarks critical of Carson.

"It is fairly remarkable to see Donald defending Ben after he called him pathological and compared him to a child molester, both of which were offensive and wrong.

"Donald didn't disagree with the substance that he supports taxpayer funding for Planned Parenthood," continued Cruz. "Donald has this weird pattern — when you point to his own record, he screams liar."

He noted Trump's previous remarks that Planned Parenthood has done "wonderful things."

Trump has argued that he was praising the organization's efforts on women's health, not abortion.

The mogul fired back, saying that that Cruz gave America ObamaCare through his support for the nomination of John Roberts to the Supreme Court, a key vote to keep the healthcare reform law in place. 

Cruz won the Iowa caucuses and Trump the New Hampshire primary. The two are now training their fire on each other in hopes of pulling ahead in the GOP race in South Carolina and beyond.