Republican National Committee chairman Reince Priebus briefed GOP members of Congress Tuesday on the process of choosing delegates to July's presidential nominating convention in Cleveland, again pushing back against implications that the process is "rigged" by party bosses, Republicans in the room tell NBC News.

In the meeting, held at the party's headquarters in D.C., Priebus underscored to lawmakers that the nominee must receive a majority of votes from the delegates - 1,237 - not a plurality, as GOP frontrunner Donald Trump has suggested. And he said that, despite charges from Trump and others that the process is "corrupt," the RNC will remain a neutral umpire without picking sides, attendees said.

The remarks echoed what Priebus told NBC News this weekend on Meet the Press, when he insisted that the eventual nominee must garner a majority of delegates in Cleveland.

"If Donald Trump, if he was winning the majority of votes, he'd likely have the majority of delegates. But that's not actually what's happening. He's winning a plurality of votes, and he has a plurality of delegates. And under the rules and under the concept of this country, a majority rules on everything," he said.