Senate Majority Leader Mitch McConnell (R-Ky.) told a Washington audience Tuesday that a brokered Republican National Convention — where no one candidate arrives with enough delegates to guarantee the nomination — is “highly unlikely to happen.”

McConnell made his comments at a breakfast event hosted by Politico at a Capitol Hill hotel. The comment came less than a week after the Washington Post reported on a meeting of top Republican officials and strategists, including McConnell and Republican National Chairman Reince Priebus, that ended with the participants resolving to prepare for the first contested national convention since 1976.

As the GOP scrambles to minimize Donald Trump's dominance in the polls, Republican leaders face the question of what would happen if no clear winner emerges. (Jenny Starrs/The Washington Post)

“It’s an interesting thing to discuss but highly unlikely,” McConnell said, noting that state laws in some cases bind how delegates can vote at party conventions.

McConnell declined to discuss what exactly was discussed at the private meeting — “I don’t have any interest in quoting myself or others” — and added that he was “appalled” that participants in the off-the-record meeting disclosed the deliberations to reporters.

“We were just talking about politics,” he said. “A bunch of politicians talking about politics.”

Later in the morning, in an interview with Fox News Channel, House Speaker Paul D. Ryan (R-Wis.) joined in trying to tamp down speculation about a messy Republican nominating contest — including speculation that Ryan himself might swoop in to claim the nomination if things remain badly unsettled in Cleveland.

“We haven’t even started the Iowa caucus yet for heaven’s sake,” Ryan said. “All this talk is ridiculous. I trust the Republican primary voter. They will sort this out … and we’ll have a good nominee.”