"Ted Cruz is a totally unstable individual. He is the single biggest liar I've ever come across, in politics or otherwise, and I have seen some of the best of them. His statements are totally untrue and completely outrageous," Trump said, days ahead of South Carolina's pivotal Republican primary.
In a statement, Trump, 69, threatened to take legal action against Cruz for him being born in Canada and not in the US.
"It is hard to believe a person who proclaims to be a Christian could be so dishonest and lie so much," he said.
"Cruz has become unhinged and is lying with the hopes that his statements will go unchecked until after the election and he will save his failing campaign," Trump alleged.
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"If Ted is going to continue to lie with such desperation, I have no choice but to fight back," he adding that one of the ways he can fight back is to bring a lawsuit against him relative to the fact that he was born in Canada and therefore cannot be President.
Cruz, 45, fired back, claiming that he is simply pointing out Trump's actual positions.
"You cannot simply scream 'liar' when someone points out your actual positions," he tweeted.
The Texas Senator said he won't engage in personal attacks, but will continue to focus on his competitor's records, policies and vision.
The Florida Senator Marco Rubio also attacked Cruz and accused him of lying.
"Senator Cruz will say or do anything to win an election including employing underhanded tactics and making charges against all his opponents that he knows are outright lies. America can't afford more politicians like Ted Cruz who will easily sacrifice principle for political gain," said Joe Pounder, Rubio spokesman.
"It is not being honest or candid for either Marco Rubio or Donald Trump to pretend that their records are different than what they are and simply to yell and scream at anyone who points to the words that have come out of their own mouths," he said.