He praised Tyler as a "good man" but said he made a "grave error of judgement."
Tyler earlier had issued an apology
late Sunday to Rubio for sharing a story on social media that featured a video misquoting the Florida senator, making it seem he made a dismissive remark about the Bible.
Rubio seized on the issue to rip his rival for what he called a pattern of "deceptive" tactics.
“Who’s going to be fired when Ted Cruz is president? Because his campaign now has repeatedly done things that they have to apologize for and no one's ever held accountable," the Florida senator told reporters earlier in the day. "Who's gonna be held accountable for making up this video?"
"Every single day something comes out of the Cruz campaign that's deceptive and untrue, and in this case goes after my faith," Rubio told
reporters in Las Vegas.
“This is a pattern now and I think we’re now at a point where we start asking for accountability,” Rubio added, acknowledging the apology from Tyler.
Tyler, who was promoting Cruz on social media on Monday afternoon, was about to appear on MSNBC when he abruptly left, according to an NBC News
The story the Cruz aide shared on social media before deleting focused on a video of Rubio walking through a hotel lobby before making a remark to a Cruz staffer.
The video quoted Rubio as saying, "Got a good book there" before quoting him in subtitles as adding, "Not many answers in it."
Rubio's campaign posted a corrected version of the video, which had unclear audio, that quoted him in subtitles as saying, "Got a good book there. All the answers in there."
Tyler in his public apology
posted to Facebook expressed regret for posting the story. He also appeared on Fox News on Monday morning, where he accepted responsibility for posting the story and called for the original video to be removed from online.
Trump, who for weeks lambasted Cruz over the Texas senator's campaign tactics in Iowa, weighed in on Twitter to claim the firing was the latest example of the Cruz campaign's "dirty tricks."
Cruz faced pressure early this month from Carson to reprimand campaign staff after aides circulated news reports on the night of the Iowa caucuses, which Cruz won, that gave the impression the retired neurosurgeon was dropping out of the GOP race.
"I don't make a practice of scapegoating staff members when it's politically convenient," Cruz said at the time, dismissing Carson's suggestion that he punish campaign staff for not circulating a follow-up report clarifying that Carson was simply taking a break from the campaign trail.