"We are not in grade school where you just get to say, 'liar liar pants on fire' and not respond to the substance," Cruz said in South Carolina on Monday.
The afternoon shot at Rubio was just the latest line from Cruz, who spent his day pushing back on his colleague's accusations of lying.
"I guess Marco's team has told him, 'Well, if anyone brings up your actual record, the fact that over and over and over again you've supported amnesty, just yell liar. Just scream, you're lying, you're lying, you're lying,'" Cruz said on "Fox and Friends" on Monday. "I guess his team has decided instead you just should insult people and claim it's a lie and they're hoping to confuse the voters."
On Sunday, Rubio accused the Texas senator of false attacks over same-sex marriage, Planned Parenthood
, immigration, campaign tactics and more.
"There's no other way to describe that -- it's a lie. When you say something that's not true, it's called a lie. That's the definition of it," Rubio said Sunday in an interview with CNN's Dana Bash on "State of the Union."
"On this campaign, he is saying things that are not true, and he's saying it repeatedly, and he knows they're not true," Rubio said.
Cruz also tried to tie the Florida senator to rival Donald Trump, saying on Fox, "Whenever anyone points to their actual record they have this strange practice of just screaming, 'liar.'"
He said both candidates were misrepresenting their records -- Rubio on immigration and Trump on his past stance on abortion, the topic of a new ad from Cruz on Monday.
And he said neither would be able to stand as commander in chief.
"I think that goes to the question of who has the experience and judgment to be commander in chief?" Cruz told reporters in South Carolina. "It makes you wonder how they would deal with (Russian President Vladimir) Putin. I'm not sure that would be very effective (at) negotiating to just scream, 'Liar, liar.' You need to have the judgment and strength to keep this country safe."
Rubio maintained his position when speaking to reporters on his campaign bus on Monday.
"I just think Ted should stop saying things that aren't true. If something isn't true that you keep saying there's no other word for it but lie. He lied about my position on marriage, lied about my position on Planned Parenthood, lied about his own record on immigration," he said. "You can't just make things up and he makes things up. He made things up about Ben Carson. It's a very disturbing pattern."
Rubio's campaign created a donations landing page
attacking Cruz for lying featuring Rubio's Sunday remarks.
In a press release detailing Cruz's "lies," the Rubio campaign continued to push the issue.
"Sen. 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," spokesman Joe Pounder said in the statement.
And his spokesmen tweeted and emailed reporters a New York Times story
reporting that anti-Rubio ads from a pro-Cruz super PAC were pulled in South Carolina after a legal review.
"This is a big deal. SC stations pulling Cruz TV ads that lie about @MarcoRubio record," Alex Conant tweeted
The two senators both need strong support from the conservative voters in the state on Saturday.
Cruz, who won the Iowa caucuses, is looking to pick up momentum to challenge front-runner Trump. And Rubio, who stumbled in New Hampshire after a strong third place in Iowa, hopes to separate himself from the other candidates to convince voters he is best positioned to challenge Cruz and Trump.