The incident comes a day before the Nevada Republican caucuses and in the wake of accusations from rival campaigns in recent weeks about Cruz's campaign tactics. Donald Trump has called Cruz a "liar" and Rubio and Ben Carson have also blasted the Texas senator.
Trump, Rubio and Carson have all attacked Cruz for his ethics ever since Cruz's victory in Iowa. Cruz later underperformed in South Carolina two contests later.
Cruz says he spent the morning investigating what happened before making his decision. Campaign manager Jeff Roe confirmed that Tyler had formally resigned.
"I have made clear in this campaign we will conduct this campaign with the very highest standards and integrity," Cruz told reporters Monday, adding that Tyler is a "good man."
"This was a grave error of judgment. It turned out the news story he sent around was false but I'll tell you, even if it was true, we are not a campaign that is going to question the faith of another candidate," Cruz said.
A former, longtime spokesman for Newt Gingrich, Tyler was a senior aide and one of the Cruz campaign's first hires in the run-up to his presidential announcement.
According to MSNBC host Kate Snow, Tyler abruptly left the studio just as he was about to go on air.
"He actually abruptly left just before we were about to go live to him and now we know why," she said on air.
Tyler had apologized late Sunday for the incident.
"I want to apologize to Sen. Marco Rubio for posting an inaccurate story about him here earlier today," said Tyler, the spokesman, wrote in a Facebook post
The latest dust-up comes as the two senators' campaigns have been clashing heatedly for days about "dishonesty" and "lies" on the trail.
Trump immediately sought to capitalize on the moment.
"Wow, Ted Cruz falsely suggested Marco Rubio mocked the Bible and was just forced to fire his Communications Director. More dirty tricks!," he tweeted.
Speaking at a campaign rally on Tuesday, Trump added that he thought Tyler was "a decent guy" but he was "taking orders from Cruz folks."
And Rubio's campaign similarly rubbed salt in the wound, praising Tyler's skills but saying he "had the unenviable task of working for a candidate willing to do or say anything to get elected."
The story mentioned by Tyler was about a video
that shows Rubio walking into a hotel lobby past Cruz's father Rafael and a staffer reading the Bible, and subtitles in the video misquote Rubio as saying, "Got a good book there, not many answers in it."
In a corrected version of the video tweeted by Rubio's communications director, Alex Conant, the subtitles quote Rubio saying, "Got a good book there, all the answers are in there."
Rubio himself explained to reporters Monday that he was saying the Book of Proverbs is especially helpful.
"I know exactly what I said to that young man. I said, 'The answer to every question you'll ever have is in that book,' and then I pointed to the Book of Proverbs, which he was reading, and then I said 'Particularly that one,'" Rubio told reporters in Nevada.
Tyler continued, "Since the audio was unclear, I should not have assumed the story was correct. I've deleted the post because I would not knowingly post a false story. But the fact remains that I did post it when I should have checked its accuracy first. I regret that mistake."
Rubio said he accepts Tyler's apology, but called for the Cruz campaign to hold someone accountable.
"It's every single day, something comes out of the Cruz campaign that's deceptive and untrue, and in this case goes after my faith. So I understand, I guess one of their spokespersons apologized and I'll accept his apology, but this is a pattern now and I think we're now at a point where we start asking about accountability," Rubio said.
The Independent Journal review first reported
the Cruz-Rubio campaign Bible controversy.
The flub by the Cruz campaign comes after Rubio finished narrowly ahead of Cruz for second place in the South Carolina primary Saturday, behind Donald Trump. In the heated contest there, the Cruz campaign was repeatedly accused by both Rubio and Trump for being dishonest and engaging in dirty tactics.
In one incident, the Cruz campaign used an altered photo
on an anti-Rubio website showing a smiling Rubio shaking President Barack Obama's hand, which was featured on a page about the "Rubio-Obama Trade Pact," accusing Rubio of casting the crucial vote to pass the Trade Promotion Authority bill in the Senate to give Obama authority to negotiate trade deals more quickly. Rubio aide Todd Harris called the photo "deceitful" in a gaggle with reporters where he distributed a printout of the page.
The Cruz campaign later changed the photo, but said it was obviously photoshopped and not an issue. They have fought back at the repeated accusations of dishonesty from the Rubio camp by saying the senator is "screaming liar" in the face of his record and spreading its own rumors.