(CNN) Ted Cruz on Tuesday unloaded on Donald Trump , accusing him during a news conference of being a "pathological liar," "utterly amoral," "a narcissist at a level I don't think this country's ever seen" and "a serial philanderer."

"He is proud of being a serial philanderer ... he describes his own battles with venereal diseases as his own personal Vietnam," Cruz said, citing a decades-old Trump appearance on "The Howard Stern Show."

The epic takedown of his opponent on an all-important voting day was extraordinary even by the standards of the 2016 campaign -- and quickly drew a scathing response from Trump.

"This man is a pathological liar, he doesn't know the difference between truth and lies ... in a pattern that is straight out of a psychology text book, he accuses everyone of lying," Cruz said as Indiana voters headed to cast their ballots.

"Whatever lie he's telling, at that minute he believes it ... the man is utterly amoral," Cruz told reporters. "Donald is a bully ... bullies don't come from strength they come from weakness."

JUST WATCHED Donald Trump implies Rafael Cruz knew JFK assassin Replay More Videos ... MUST WATCH Donald Trump implies Rafael Cruz knew JFK assassin 01:29

Trump trashes Cruz's dad

Earlier Tuesday, Trump had criticized Rafael Cruz, calling him "disgraceful" after he urged evangelical voters in Indiana to reject his son's rival.

Trump also referenced a report from the tabloid National Enquirer -- without naming the publication -- which alleged that it had identified Rafael Cruz in a photo with Lee Harvey Oswald months prior to the JFK assassination. CNN has not independently confirmed that report -- and there is no evidence that it is true.

JUST WATCHED Trump pushes tabloid nonsense about Cruz's father and JFK assassination Replay More Videos ... MUST WATCH Trump pushes tabloid nonsense about Cruz's father and JFK assassination 03:34

"And (Ted Cruz's) father, you know, was with Lee Harvey Oswald prior to Oswald's, you know, being shot. I mean the whole thing is ridiculous," Trump said in an interview on "Fox and Friends." "I mean what was he doing with Lee Harvey Oswald, shortly before the death? Before the shooting? It's horrible."

The remark led to swift criticism from some establishment Republican figures.

South Carolina Sen. Lindsey Graham, a fierce opponent of Trump, tweeted, "Any doubt left Trump is completely unhinged? His assertion Ted Cruz's father was associated with Lee Harvey Oswald should remove ALL doubt."

Any doubt left Trump is completely unhinged? His assertion Ted Cruz's father was associated with Lee Harvey Oswald should remove ALL doubt. — Lindsey Graham (@LindseyGrahamSC) May 3, 2016

And Mark Salter, a top aide to 2008 Republican presidential nominee John McCain, tweeted that he'd back Hillary Clinton over Trump.

"The GOP is going to nominate for President a guy who reads the National Enquirer and thinks it's on the level. I'm with her," Salter said.

'A very angry man'

Trump responded with a statement Tuesday afternoon calling Cruz "unhinged" and "desperate" as his losses to Trump have mounted.

"Today's ridiculous outburst only proves what I have been saying for a long time, that Ted Cruz does not have the temperament to be president of the United States," Trump said.

He followed up early Tuesday evening by tweeting, "Wow, Lyin' Ted Cruz really went wacko today. Made all sorts of crazy charges. Can't function under pressure - not very presidential. Sad!"

Wow, Lyin' Ted Cruz really went wacko today. Made all sorts of crazy charges. Can't function under pressure - not very presidential. Sad! — Donald J. Trump (@realDonaldTrump) May 3, 2016

Trump's senior campaign adviser Barry Bennett downplayed Cruz's emotional outburst as a response to Trump and called it evidence of Cruz's failing campaign headed into primary night.

"We're watching his campaign implode, we're watching his reputation be torn to shreds ... he's a very angry man right now," Bennett told CNN's Kate Bolduan on "At This Hour," calling it a "truly sad display."

Trump's son, Donald Trump Jr., also tweeted the move was "desperate" and called it childish.

"That was an impressive meltdown... Desperate but impressive. Reminded me of my 3 year old coming off a sugar high," he wrote

That was an impressive meltdown... Desperate but impressive. Reminded me of my 3 year old coming off a sugar high. https://t.co/3lqwHIRWo6 — Donald Trump Jr. (@DonaldJTrumpJr) May 3, 2016

JUST WATCHED Latest Cruz, Trump battle over their wives Replay More Videos ... MUST WATCH Latest Cruz, Trump battle over their wives 04:13

Not the first time

It's not the first time the two candidates have come to verbal blows over a spat involving Cruz's family members.

Trump and Cruz exchanged accusations about each other inappropriately going after the candidates' wives in March, when Trump retweeted an unflattering picture of Heidi Cruz next to a flattering picture of his model wife, Melania. Trump also ambiguously threatened to "spill the beans" on Heidi.

Cruz responded angrily, calling Trump a "sniveling coward" and telling him to "leave Heidi the hell alone."

The National Enquirer -- which endorsed Trump -- has also run recent stories making various allegations about the billionaire businessman and about his rival that have not been confirmed by CNN or other publications.

The Cruz campaign responded to Trump by calling him "detached from reality."

"His false, cheap, meaningless comments every day indicate his desperation to get attention and willingness to say anything to do so," said Catherine Frazier, Cruz's campaign spokeswoman in a statement. "We are campaigning on jobs freedom and security while Trump campaigns on false tabloid garbage. And the media is willfully enabling him to cheapen the value of our democratic process."