House Select Committee on Benghazi Chairman Trey Gowdy, R-S.C. (AP Photo/Cliff Owen)

Updated with statement from Gowdy

A long-simmering campaign to draft Rep. Trey Gowdy into a House leadership post suddenly re-emerged Tuesday in the scramble following House Speaker John A. Boehner’s resignation. But Gowdy extinguished those hopes late in the day, leaving conservatives to continue their search for a standard-bearer.

“I am staying on the Benghazi committee, period, exclamation point,” he said just before 4 p.m. Tuesday.

Calls to pull Gowdy into the race for majority leader began to rapidly pick up momentum Tuesday morning, with several Republican members from across the ideological spectrum saying they have personally asked the South Carolina Republican to jump into the contest.

Rep. Jason Chaffetz (R-Utah), chairman of the House Oversight and Government Reform Committee and a Gowdy friend, kicked off the calls in a morning Fox News Channel appearance: “If you want the best person to make the Republican case, if you want the best person to talk about why conservatism is the right answer for America, Trey Gowdy is our best foot forward.”

But Gowdy, the former state and federal prosecutor best known for chairing the House Select Committee on Benghazi, moved to tamp down the draft discussion and eventually squelched it entirely — in keeping with previous occasions where he has shied away from any sort of leadership run, even as his national profile has skyrocketed.

Asked if he had been close to pursuing a run, Gowdy said, “not really.”

“Have I ever run for a leadership position?” he said. “I’ve never run for one.”

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A close ally who had been among those floating Gowdy’s candidacy, Rep. Mick Mulvaney (R-S.C.), tweeted earlier Tuesday afternoon that Gowdy “made it clear that he is OUT of any consideration for any leadership position” in the course of a 20-minute discussion.

But rumors continued to course through the Capitol that Gowdy might run, harnessing conservatives’ hopes that one of their own might be able to break into the leadership ranks. At 1:30 p.m., shortly after Mulvaney’s tweet, Chaffetz was insisting to reporters that Gowdy was in.

“I think if the conference wants him to serve, he will,” said an optimistic-sounding Chaffetz. “Trey Gowdy is not the kind of person who’s going to go out and overtly campaign for it. But if the conference rallies behind him, I think he would reluctantly serve. I, and a lot of others, think he would do the best job of uniting our conference and making our case to the American people.”

House Republicans are facing a leadership reshuffle within their ranks — but as some lawmakers pull the party more toward the right, can any leader really restore unity? The Post's Robert Costa takes us inside the infighting in the Capitol. (Julie Percha/The Washington Post)

Gowdy’s panel is also deeply involved in investigating Hillary Clinton’s use of a private e-mail server as secretary of state, and the Democratic presidential candidate will testify before the select committee on Oct. 22, promising to shine the biggest spotlight of his career on the lawmaker.

Rep. Mia Love (R-Utah), a first-term member who identifies with the tea party movement, endorsed Gowdy for majority leader in a morning statement as someone who “is respected across the political spectrum and will help create clarity and focus for Republicans to lead the country into a better, brighter future.”

“He is the kind of smart fighter our country needs and the American people deserve,” Love said in the statement. “With impressive communication skills, genuine compassion and the tenacity of a prosecutor, he will unite the party and the people around a truly American agenda.”

[After Boehner, conservatives must answer crucial question: Who’s next?]

The scuttlebutt continued as House Republicans gathered at the Capitol for a morning meeting to begin sorting out who should comprise their new leadership team following Boehner’s announcement Friday that he will resign at the end of October.

Mulvaney said after the meeting that interest in Gowdy was rising because the current candidates for majority leader — House Budget Chairman Tom Price (R-Ga.) and current GOP Whip Steve Scalise (R-La.) — are fighting a hotly contested battle and some members may like to see another voice enter who could emerge as a consensus pick.

“If there is a race for majority leader, and it becomes something that we can’t settle easily, if it becomes divisive, Trey is [somebody] who I think a lot of folks could rally behind as sort of a fallback position,” Mulvaney said.

He added, “He’s not actively running. He’s saying, ‘Look, if this doesn’t work out, come talk to me.'”

Love said after the conference meeting that she spoke to Gowdy Monday night and left the conversation believing he might be open to a run: “I absolutely think he’ll do it. If he’s called to serve, I think he’ll serve.” Chaffetz said on Fox he had spoken to Gowdy about a leadership run and said, “I actually think he’ll do it if we get behind him and support him.”

The Tea Party Leadership Fund launched a Draft Gowdy campaign ahead of January’s speaker election, but he disclaimed any interest in challenging Boehner (R-Ohio).

Gowdy is a member of the Republican class of 2010, sent to Washington in a wave election fueled by tea party groups and other conservative activists outraged over Obamacare. His ascension to leadership would mark a generational milestone in a GOP caucus where well over half of members have served three terms or less.

He was elevated to the Benghazi chair panel in May 2014 and has served as an aggressive antagonist of Clinton, earning kudos from his colleagues and right-wing activists in the process.

But Democrats charge that the committee has morphed into a panel to investigate the Democratic presidential frontrunner. Pursuing more information about Benghazi and whether lawmakers have seen the full e-email record, Gowdy summoned in early September former top Clinton staffers Cheryl Mills and Jake Sullivan. He has also been trying to compel testimony by Brian Pagliano, the ex-State IT staffer who managed the server, but Pagliano has so far taken the Fifth Amendment.

[Staffer who worked on Clinton’s private e-mail server faces subpoena]

Scalise and Price have both been gathering support for days, seeking to contact each of the nearly 250 other Republicans who will pick the new leadership slate. One member, Rep. Lynn Westmoreland (R-Ga.), said it might be too late for Gowdy to make an impact on the majority leader race.

“Anybody can run, but this is probably a little late in the process,” said Westmoreland, who said he had already pledged his support to one of the declared candidates in the race. “These guys [Price and Scalise] have been calling folks for a long, long time. There’s a lot of commitments already made.”

Boehner on Tuesday said he has not yet determined when to call leadership elections but said he “would hope to make an announcement in the next day or two about that.” A longer campaign period — perhaps even beyond the scheduled weeklong congressional recess scheduled for Oct. 12 to 16 — could help erode any advantage built by Price and Scalise.

David Weigel contributed to this post.