Leaders of the Republican establishment, alarmed by the emergence of far-right and often unpredictableTea Party candidates, are pushing their party to rethink how it chooses nominees and advocating changes they say would result in the selection of less extreme contenders.

The push comes as the national Republican Party is grappling with vexing divisions over its identity and image, and mainstream leaders complain that more ideologically-driven conservatives are damaging the party with tactics like the government shutdown.

The debate intensified on Wednesday after Kenneth T. Cuccinelli II, the deeply conservative Republican candidate for governor of Virginia, lost a close race in which Democrats highlighted his opposition to abortion in almost all circumstances, his views on contraception and comments in which he seemed to liken immigration policy to pest control.

The party leaders pushing for changes want to replace state caucuses and conventions, like the one that nominated Mr. Cuccinelli, with a more open primary system that they believe will draw a broader cross-section of Republicans and produce more moderate candidates.

Similar pushes are already underway in other states, including Montana and Utah, and last week Mitt Romney said Republicans should consider how to overhaul their presidential nominating process to attract a wider range of voters. He suggested that states holding open primaries be rewarded with more delegates to the party’s national convention.

While the discussion may appear arcane, it reflects a fierce struggle for power between the activist, often Tea Party-dominated wing of the Republican Party — whose members tend to be devoted to showing up and organizing at events like party conventions — and the more mainstream wing, which is frustrated by its inability to rein in the extremist elements and by the fact that its message is not resonating with more voters.

“Conventions by nature force candidates and campaigns to focus on a very small group of party activists,” said Phil Cox, executive director of the Republican Governors Association and a longtime Virginia-based strategist. He grimaced at the successful movement by conservative activists in his state earlier this year to switch from a primary system to a convention system. “If the goal is actually to win elections, holding more primaries would be a good start.”

With control of the Senate expected to turn on a handful of races around the country next year, Republican leaders are worried about the outcome in Iowa, where a crowded field of G.O.P. candidates has taken shape, including several untested ones. If no one receives 35 percent of the primary vote, the nominee will be selected by a convention.

“Conventions have a flimsy track record of selecting the most electable candidates,” David Kochel, an Iowa-based Republican strategist, said in an interview on Wednesday. “There’s just no good substitute for a full-scale vetting by a large universe of primary voters.”

Nowhere is the debate over how to limit the influence of the party’s most hard-line activists more intense than in Utah, where in 2010 conservatives cheered as the Tea Party toppled one of the veteran Republican centrists in the Senate, Bob Bennett. The state party’s caucus and convention system helped elevate Mike Lee, a little-known lawyer who replaced Mr. Bennett.

Now Mr. Lee is a patriarch of sorts to Tea Party conservatives in Congress. Though Senator Ted Cruz of Texas was the public face of the government shutdown fight, it was Mr. Lee who largely conceived the strategy in an effort to block funding for President Obama’s health care law.

Back home, Mr. Lee is now at odds with Republican stalwarts like former Gov. Mike Leavitt, who are leading a campaign for a ballot initiative that would shift the state to a primary system where party conventions have no role in picking candidates and, instead, all Republicans can participate.

“If you look at the place where the aggregate heart of the Republican Party is in this state, it is not represented by the aggregate of folks who attend conventions — demographically or ideologically,” Mr. Leavitt said in an interview this week.

The Republican Party in Utah picks its candidates for statewide office, like United States Senate, at a convention of about 4,000 delegates who are chosen at a series of caucuses all over the state.