US Republican presidential candidate Ted Cruz has addressed his growing credibility gap by sacking his communications director for issuing a false video that accused rival Marco Rubio of disparaging the Bible.

It was an awkward move a day before the Nevada caucus.

The sacking is the latest indication that the Texas senator is concerned about the mounting attacks against him, first launched by front-runner Donald Trump, that he plays fast and loose with the truth and is a master of dirty tricks.

Communications director Rick Tyler was forced to apologize after posting a story on Facebook that falsely claimed Rubio told Cruz's father that the Bible didn't "have many answers" in it.

The story included a video with inaccurate subtitles. In fact, Rubio was praising the Bible and said the book has "all the answers."

"I've spent this morning investigating what happened, and ... I asked for Rick Tyler's resignation," Cruz told reporters at a news conference in Las Vegas. "I have made clear in this campaign that we will conduct this campaign with the very highest standards of integrity."

Cruz called Tyler a "good man," but said the Facebook story was "a grave error in judgment."

Rubio's campaign immediately stepped up to blast Cruz's credibility.

"Rick is a really good spokesman who had the unenviable task of working for a candidate willing to do or say anything to get elected," Rubio communications director Alex Conant told the Daily Beast. "There is a culture in the Cruz campaign, from top to bottom, that no lie is too big and no trick too dirty."

Rubio's campaign had earlier complained about a doctored photograph used by the Cruz campaign that suggested Rubio had shaken hands with President Obama over a controversial trade pact.

Trump, too, took the opportunity to say "I told you so." He first called Cruz a liar in the run-up to the Iowa caucuses when Cruz accused him of supporting the Obamacare health insurance program.

At a press conference before the South Carolina primary he called his rival a liar six times in 90 seconds, noting: "He's the single biggest liar I've ever seen."