For the next few minutes, the Texas senator unleashed a blitz of personal attacks on a variety of fronts.
Cruz called Trump a "pathological liar" who "doesn't know the difference between truth and lies. He lies practically every word that comes out of his mouth."
He said the mogul is "utterly amoral" and "terrified by strong women." He predicted that Trump "will betray his supporters on every issue." And he said Trump is "proud of being a serial philanderer."
"I want everyone to think about your teenage kids," Cruz said. "The president of the United States talks about how great it is to commit adultery, how proud he is. Describes his battles with venereal disease as his own personal Vietnam. That’s a quote, by the way, on the Howard Stern show. Do you want to spend the next five years with your kids, bragging about infidelity? Now what does he do? He does the same projection, just like a pathological liar. He accuses everyone of lying."
In his book "The Art of the Comeback," Trump wrote: "If I told the real stories of my experiences with women, often seemingly very happily married and important women, this book would be a guaranteed best-seller."
Earlier in the day, Trump said Cruz's father, Rafael Cruz, was spotted with Lee Harvey Oswald around the time of the murder of President John F. Kennedy. He appeared to be referencing a photo published last month by the National Enquirer that shows Oswald and another man distributing pro-Castro leaflets in New Orleans in 1963.
Cruz and his campaign vigorously denied that the photo was of his father.
"I will say this: This morning, Donald Trump went on national television and attacked my father. Donald Trump alleges that my dad was involved in assassinating JFK. Now let's be clear, this is nuts. This is not a reasonable position," said Cruz.
Cruz sarcastically said his dad killed Kennedy. "He is secretly Elvis and Jimmy Hoffa is buried in his back yard," he added.
Public polls show Trump is heavily favored to win in Indiana today.
In a statement responding to Cruz, Trump said the senator "is a desperate candidate trying to save his failing campaign. It is no surprise he has resorted to his usual tactics of over-the-top rhetoric that nobody believes."
Jose A. DelReal contributed to this report.