The Republican presidential contender told radio host Hugh Hewitt that Democrats -- aided by a "salivating" media -- attempt to use mass killings to damage conservatives politically.
His comments came as Cruz discussed the shootings at a Planned Parenthood clinic in Colorado -- which Democrats have followed with calls for the GOP to stop denouncing the organization and pushing for its defunding on Capitol Hill.
"Every time you have some sort of violent crime or mass killing, you could almost see the media salivating, hoping desperately that the murderer happens to be a Republican so they can use it to try to paint their political enemies," Cruz said.
He continued: "Now, listen, here's the simple and undeniable facts: The overwhelming majority of violent criminals are Democrats. The media doesn't report that."
Asked for evidence to support that claim, Cruz's campaign cited research by the University of Pennsylvania's Marc Meredith and Stanford University's Michael Morse, which found that ex-felons who register to vote have, in the states the researchers examined, overwhelmingly registered as Democrats.
In their study, published in the January 2014 edition of "The Annals of the American Academy of Political and Social Science," Meredith and Morse also cite previous research that showed felons are more likely to be Democrats based on factors like ethnicity, income, age, employment, marital status and education.
Cruz said that Democrats "for years have been viewed as soft on crime" because judges appointed by the party's executives have released violent criminals.
"They go in and fight to give the right to vote to convicted felons. Why? Because the Democrats know convicted felons tend to vote Democrat, and so the media never reports on any of that and doesn't want to admit any of that but you can see in every one of these -- every time there's a terrible crime, they're so excited, 'Come on, please one of these be a Republican so we can try to paint the other side,'" Cruz said. "It is one of the more egregious examples of media bias but it's something we see over and over and over again."
The issue of criminal sentencing reform has come up during the 2016 presidential race. Several Republican candidates, including Kentucky Sen. Rand Paul, have advocated shorter prison sentences and alternative methods for non-violent offenders.