The spat comes as RNC Chairman Reince Priebus has been playing defense for more than a week, beating back charges from Trump that the party has "rigged" the nominating fight against him.
"Lyin' Ted Cruz can't get votes (I am millions ahead of him) so he has to get his delegates from the Republican bosses. It won't work!" Trump tweeted Sunday.
Republican National Committee Rules Chairman Bruce Ash, who is part of a group of conservatives who want to openly debate rules changes when they meet in a few days, on Saturday accused the party's top lawyer, John Ryder, of attempting to stifle that debate and a "breach of trust" in an email obtained by CNN.
But Ryder, who is supporting Priebus' efforts, replied that it had been a misunderstanding. He cautioned in a reply email that "it is important that the RNC not take action that can be interpreted as attempting to favor one candidate or another ... Major changes now are dangerous and not a good idea, in my humble opinion."
On Sunday, Priebus echoed Ryder's position. He said given the "politically charged environment" it doesn't make sense for the RNC's rules panel to recommend any changes to the current nomination process, particularly because the delegates in Cleveland will ultimately decide how to go about it anyway.
"I don't think that it's a good idea for us next week, I mean, before the convention to make serious rules changes or recommendations of changes right now," he told CNN's Dana Bash on "State of the Union." "I think it's too complicated. I think that the RNC Rules Committee, going forward, with making rules suggestions is not a good idea."
Responding to Trump's accusations, Priebus said: "I don't sit here and internalize the charge because there's no there there because there's nothing the RNC can do about it."
Trump's complaints come as his rival, Ted Cruz, has managed to engineer a highly successful delegate operation, in some cases netting him additional delegates or getting friendly ones elected who could switch their support to him in the event of a contested convention.
If the Rules Committee declines to offer a recommendation on the nomination process, it would break with tradition. In most previous elections the RNC rules panel has sent its thoughts to the convention panel, where they were then approved without much debate.
The committee is set to meet Thursday in Hollywood, Florida.
"Obviously the chairman (Priebus) correctly has concluded that any changing of the rules, even changing a comma or a semicolon at this point in time would be perceived by some as a conspiracy to cheat somebody," said Curly Haugland, a member of both the party and convention rules committees.
Ash did not immediately respond to a request for comment Sunday. Ryder directed questions to Republican Party communications director and top strategist Sean Spicer, who said Ryder's reply speaks for itself.
At the center of the most recent fight is a push by conservatives on the Republican National Committee to have Robert's Rules of Order govern the convention instead of the rules of the U.S. House. It sounds arcane, but conservative RNC members argue the change is needed to prevent party establishment figures from pushing through someone like House Speaker Paul Ryan in the convention.