"It's clearly not (rigged)," he told CNN's Wolf Blitzer on "The Situation Room." "Look, all the candidates have the rules of the game. There were no complaints about that system, at least not in Colorado."

Trump said during CNN's family town hall Tuesday that the party's rules are "stacked against me," and accused the RNC of conspiring against him.

"I have to respond when the party I'm chairman of is being attacked. It's just not true," Priebus said, adding that the Trump campaign and the RNC are talking daily.

"This is going to blow over. I believe this is some frustration that has bubbled up," the chairman said, adding that he doesn't take the attack personally.

"The rules are not being changed," Priebus said.

JUST WATCHED Donald Trump slams 'rigged' system after Colorado loss Replay More Videos ... MUST WATCH Donald Trump slams 'rigged' system after Colorado loss 01:19

Fraught relationship

The relationship between Trump and Priebus has been tenuous almost since Trump announced his campaign, including periods of disagreement and détente.

Trump's latest assault on the Republican Party -- and specifically Priebus -- came in an interview with The Hill newspaper published before Tuesday's CNN town hall.

"It's a disgrace for the party. And Reince Priebus should be ashamed of himself," Trump told the Hill.

Trump alleges that the byzantine party rules -- which vary from state to state -- for selecting delegates to send to the national convention have been unfairly exploited by rival Ted Cruz, specifically in Colorado and Louisiana

"He should be ashamed of himself because he knows what's going on," Trump told The Hill of Priebus.

Trump later told CNN's Anderson Cooper that he suspects the party doesn't want him to win the nomination and is conspiring against him.

Priebus swiftly responded to Trump's claims.

"Nomination process known for a year + beyond. It's the responsibility of the campaigns to understand it. Complaints now? Give us all a break," Priebus tweeted, without naming Trump.

Nomination process known for a year + beyond. It's the responsibility of the campaigns to understand it. Complaints now? Give us all a break — Reince Priebus (@Reince) April 13, 2016

JUST WATCHED Donald Trump meets with RNC chair in Washington Replay More Videos ... MUST WATCH Donald Trump meets with RNC chair in Washington 01:23

Cordial meeting

The spat emerged less than two weeks after Priebus and Trump met in Washington , after which Trump tweeted praise for the RNC chief.

"Just had a very nice meeting with @Reince Priebus and the @GOP. Looking forward to bringing the Party together --- and it will happen!" Trump tweeted.

Just had a very nice meeting with @Reince Priebus and the @GOP. Looking forward to bringing the Party

together --- and it will happen! — Donald J. Trump (@realDonaldTrump) March 31, 2016

The Trump campaign has also said the candidate is set to embark on a series of speeches more focused on policy and other themes, in addition to his typical free-wheeling rallies. The first is said to be on preaching party unity.

JUST WATCHED Trump renounces pledge to support GOP nominee Replay More Videos ... MUST WATCH Trump renounces pledge to support GOP nominee 01:03

Party loyalty

Trump had intermittently stood by that pledge since he launched his campaign last summer, leaving Priebus the unenviable task of courting both the party's front-runner and maintaining control of the at-times fractious nomination process.

In the wake of a particularly vitriolic debate in early March -- which involved references to candidates' body parts -- the RNC chair sought to preach civility.

"I think the tone should improve. And I would hope that at the next debate, things are improved over the last debate as far as tone and rhetoric," Priebus had said

While Trump has repeatedly suggested that the RNC has not been supportive of him, Priebus has said that leaders will ultimately back whoever the nominee is -- even if it is Trump.