The move comes on the even of the Republican caucuses in Nevada and as rival campaigns have piled on Cruz for his alleged lies and "dirty tricks."
Cruz's national spokesman Rick Tyler had shared on Facebook a story from University of Pennsylvania student newspaper The Daily Pennsylvanian, which reported that Rubio told a Cruz staffer reading the Bible that the holy book did "not have many answers in it."
Tyler later deleted the post and apologized to Rubio for posting the "inaccurate" story.
The issue strikes to the heart of Cruz's support among evangelical Christians. The Texas senator has also spoken openly about his own faith.
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"This was a grave error of judgment," Cruz said during a campaign event yesterday while also praising his spokesman as "a good man."
"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.
Rubio told reporters he accepted the Cruz campaign's apology, but called for more "accountability."
"It's every single day something comes out of the Cruz campaign that's deceptive and untrue," Rubio said, calling the Bible video "perhaps the most offensive" Cruz tactic to date because it questioned his faith.
"I know exactly what I said to that young man," Rubio told reporters. "I said the answer to every question you'll ever have is in that book.