Washington (CNN) Republican presidential hopeful and former US Rep. Joe Walsh said Monday he regrets falsely claiming former President Barack Obama was Muslim in 2016 tweets.

Walsh insisted "there was nothing derogatory meant by" the claim, but told CNN's Erica Hill on "The Lead" he apologizes for his comments, saying it was "wrong."

The former Illinois congressman, who recently announced he will challenge President Donald Trump for the 2020 Republican presidential nomination , accused Obama in 2016 of hating Israel and said the reason was because he is Muslim.

The conservative radio host, who was elected to Congress with support from the Tea Party, was also accused that year of inciting violence against Obama in the wake of a deadly sniper attack on Dallas police.

Walsh said earlier Monday he's running against Trump "to make the moral case against him."

"Look, I have been waiting every single day this year for somebody to step up, a Republican to step up, to make the moral case against him. That he is unfit," Walsh told CNN's Alisyn Camerota on "New Day." "Come on -- somebody should challenge him."

On Sunday, Walsh announced he will challenge Trump and told ABC News in an interview that "the country cannot afford to have him win." Walsh said he won't vote for the President if Trump again wins the party's nomination.

Walsh, on Monday and in the weeks leading up to his announcement, apologized for what he said was his role in helping elect Trump in 2016 and for how controversial tweets he previously made may have helped "lead to what we have now in the White House."

Asked by Camerota about his incendiary tweets, Walsh defended his Twitter habits, saying his "impulse is to push the envelope and to get people to think."

"I just want to remind people: even if you don't agree with me, we live in a country where we do have free speech," he said, adding, "Oftentimes, Alisyn, I step over the line ... If there's one thing I've learned in the last couple years (it) is it can lead to what we have in the White House now."

Walsh also said his radio callers probably do not think he can beat Trump in the primary, but added that his campaign is about being "brave" and that his bid is "a bet I'm making."