Backed by evangelical voters and riding a wave of anti-Washington sentiment, Roy Moore is surging in the Republican primary runoff in Alabama’s special U.S. Senate election, threatening to upend the GOP establishment.

Mr. Moore, the former chief justice of Alabama’s Supreme Court, holds a lead over Sen. Luther Strange in the latest polling, and won the backing this week of a political action committee that boosted President Trump in last year’s campaign.

But the endorsement by Great American PAC is all the more stunning because Mr. Trump has endorsed Mr. Strange in the race — adding another layer of intrigue to a GOP contest that has been all about who is going to be most loyal to the commander-in-chief.

Things got messier Thursday after the Strange campaign released a poll, conducted by the super PAC tied to Senate Majority Leader Mitch McConnell, showing Mr. Moore leading by a single percentage point — a finding that ran against the latest Real Clear Politics average of surveys, which has Mr. Moore up by 11 points.

GOP voters go to the polls Sept. 26, and the winner will face Democrat Doug Jones, a former U.S. attorney, in the general election in December. The Republican nominee likely will be favored to win in conservative Alabama.

“Judge Roy Moore has been standing up for great American principles for years — he’s completely unafraid of the establishment ‘swamp creatures’ lurking in Washington,” said Ed Rollins, chairman of the Great American PAC. “He’s the leader we need in the Senate working with President Trump to enact the America First agenda.”

The White House this week, though, said Mr. Trump still stands behind Mr. Strange, who has held the seat since he was appointed in February to take the place of former Sen. Jeff Sessions, who left the chamber to become attorney general.

Mr. Trump remains the overriding issue, with both candidates rushing to embrace him — even if they don’t always agree with what he’s doing.

Last week, the president blindsided GOP leaders on Capitol Hill by striking a deal to increase the government’s debt, keep the government open into December and speed emergency relief to victims of Hurricanes Harvey and Irma.

Mr. Strange backed the deal, while Mr. Moore said he would have opposed it. But Mr. Moore blamed Senate Majority Leader Mitch McConnell for the deal, not Mr. Trump, despite the Kentucky Republican having been cut out of the deal-making.

The Senate Leadership Fund, the political action committee aligned with Mr. McConnell, has funneled millions of dollars into the primary, helping to dent another GOP candidate who came in third in last month’s primary.

Mr. Moore came out on top in the primary, but fell short of winning 50 percent of the vote, setting up the runoff with Mr. Strange, who came in second.

Since then, the pro-McConnell forces have turned their fire against Mr. Moore, who has vowed to support Mr. Trump’s “America First Agenda.”

Mr. Trump hasn’t announced any plans to assist Mr. Strange.

But his former top strategist, Breitbart chief Stephen K. Bannon, is backing Mr. Moore.

Mr. Moore also has recently racked up endorsements from a number of conservative stalwarts on Capitol Hill — including the chairman of the House Freedom Caucus, Rep. Mark Meadows of North Carolina, and a co-founder of the group, Rep. Jim Jordan of Ohio.

Still, it’s Mr. Strange who’s seen as the establishment’s man in the race, backed by Mr. McConnell and Mr. Trump.

John Couvillon of JMC Analytics and polling said Mr. Moore has deep support among evangelical Christians, as well as from voters that are either searching for a candidate following the primary and or struggling to stomach Mr. McConnell’s influence on the race.

“You have to make the argument that the outside support for Sen. Strange is also driving Moore’s electoral surge,” Mr. Couvillon said. “Alabama is a state where having that evangelical support is pretty crucial to have if you want to win. This is not like running in Oregon or California.”

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