In an escalation of mutual distrust among top party members, a Republican National Committee official will formally move to block House Speaker Paul D. Ryan from possibly thwarting Donald Trump’s nomination, The Washington Times has learned.

Bruce Ash, chairman of the national party’s powerful rules committee, will petition to amend the “40d” rule to bar the counting of votes in the televised roll call of states for candidates who are not on the convention ballot. Mr. Ash’s proposal would “close and lock the back door to a hijacking of the nomination” by the small but tenacious #NeverTrump and “vote your conscience” factions.

Mr. Ryan is expected to preside over the Cleveland convention as its chairman, chief shot-caller and final arbiter.

Although he has not said he would use his power to deny Mr. Trump the nomination, he has repeatedly criticized Mr. Trump and told fellow House Republicans that they should vote their conscience in November. Many Republicans regard that advice as treasonous aid to Democrat Hillary Clinton by encouraging people not to back Mr. Trump.

Mr. Ash, who says Mr. Trump was not his first, second or even third choice for the nomination, nonetheless argues that Mr. Trump won the nomination fair and square.

“Why do I distrust [RNC Chairman Reince Priebus] and the rest of the leadership?” Mr. Ash said. “Because as the RNC Standing Rules Committee chairman, I asked for a public pledge to support our presumptive nominee. I asked this from Reince, his convention leadership team, the various chairmen of the standing committees and from the convention committee chairman. I never heard back from anybody.”

Mr. Ash said he is distrustful as well because the “RNC doesn’t appear to be publicly defending our presumptive nominee against those ‘vote your conscience’ and #NeverTrump factions.”

Wisconsin Gov. Scott Walker has told his state’s delegates that they should vote their conscience even though six of the 42 are bound by their primary election’s results to vote for Mr. Trump on the first ballot.

Rules committee member Solomon Yue of Oregon said leaders of a “vote your conscience” faction have named a proposed change “the Ryan-Walker amendment.”

Another cause of distrust is Mr. Priebus’ hiring as a convention whip former Texas Republican Party Chairman Steve Munisteri, who was on the Rand Paul campaign until it folded.

Mr. Munisteri has been making calls to committee members offering various interpretations of the rules. One such interpretation indicated that votes could be counted for someone whose name is not on the convention ballot, making that person the presidential nominee by winning a majority of delegate votes.

The rule under which all 17 original Republican nomination contestants competed said that to get on the convention ballot, a candidate would have to win a majority of delegates from eight states during the primaries and caucuses.

Only Mr. Trump and Sen. Ted Cruz have qualified, so only their names will be on the convention ballot unless shenanigans materialize.

Mr. Ash has publicly questioned Mr. Priebus’ naming of two Mitt Romney acolytes — Utah RNC member Enid Mickelsen and Massachusetts RNC member Ron Kaufman — to be chairwoman and co-chairman, respectively, of the convention rules committee. That panel considers and makes final calls on recommendations from Mr. Ash’s committee.

Mr. Romney has led the #NeverTrump movement.

Mr. Ash also has questioned Mr. Priebus’ naming of a heavy-hitter in the Republican establishment, former Mississippi Gov. Haley Barbour, to head another powerful committee — on permanent convention organization.

Mr. Priebus did not respond directly to Mr. Ash’s comments, but the chairman’s top aide, RNC chief strategist Sean Spicer, said in an email, “It’s sad to see people make up faux controversies instead of focusing all of the energy on keeping Hillary Clinton out of the White House.”

While Mr. Priebus has declared Mr. Trump the presumptive Republican presidential nominee, national party chairmen must consider a plan B in case something goes awry before the convention.

The suspicion among RNC members such as Mr. Ash, Mr. Yue and committee counsel James Bopp is that Mrs. Mickelsen, Mr. Kaufman and Mr. Barbour were handed powerful roles in case Mr. Priebus decides that the rules need to be changed so delegates aren’t bound to a particular candidate on any ballot. Current rules bind them on the first ballot.

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