Leaders of the Republican establishment, alarmed by the emergence of far-right and often unpredictable Tea Party candidates, are pushing their party to rethink how it chooses nominees and advocating changes that 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 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 compare immigration policy to pest control.

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

Similar pushes are underway in other states, including Montana and Utah, and last week Mitt Romney said Republicans should re-examine 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 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 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 GOP 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 Wednesday.

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 Bennett.

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

Back home, 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.

"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," Leavitt said in an interview this week.

The Republican Party in Utah picks its candidates for statewide office, including U.S. Senate, at a convention of approximately 4,000 delegates chosen at a series of local caucuses all over the state.

Supporters of the system argue that representation is ample on the front end, when thousands of people are involved in selecting convention delegates whom they get to know through the intimacy of a local caucus. Candidates for office, in turn, have to campaign directly to those delegates.

Efforts to dismantle the convention system, they say, are elitist and undemocratic.

"You have these politicians who really think they’re above everybody else," said Paul T. Mero, president of the Sutherland Institute, a research organization in the state. "What they want certainly isn’t the kind of direct democracy that really requires responsible citizenship. They want to get rid of that, and move straight to a primary where it’s all about money and name recognition."

In Virginia last year, state Republican leaders switched their system for selecting a nominee for governor from a primary to a convention, a decision that all but guaranteed that Cuccinelli would be the party’s choice. It was a sudden turn of events that doomed the more moderate candidate, Lt. Gov. Bill Bolling.

Bolling and his allies in the party had persuaded their state board to hold a primary that would be open to all voters. Outraged conservatives, many of them loyal to the former presidential candidate Ron Paul, captured slots on the board and reversed the decision.

Their maneuver resulted in a slate of far-right candidates at the top of the ticket, including the lieutenant governor nominee, a minister named E.W. Jackson who has a history of inflammatory remarks, such as when he compared Planned Parenthood to the Ku Klux Klan and associated homosexuality with pedophilia.

To revert back to a primary system would be difficult but not impossible, Republicans in the state said this week, especially given the soul-searching that Cuccinelli’s loss has inspired.

"The convention method is political arsenic, pure and simple," said Mike Murphy, a veteran Republican consultant. "It incentivizes our candidates to appeal to the base voters they already get for free, not the swing voters they need to win."

Republican leaders in Montana, struggling with how to manage their state’s far-right elements, have put an initiative on the ballot that would replace their current primary process with a system that would allow only the top two candidates to move on to the general election, regardless of party.

Last year Republicans narrowly lost a hard-fought Senate race after a former Republican local committeeman ran on the Libertarian ticket and, many believe, drew votes away from the GOP, tipping the race to Sen. Jon Tester, a Democrat.

The goal, Republicans said, is the same as in Utah and Virginia. Art Wittich, the majority leader in the state Senate, said that if approved the measure would stop fringe candidates.

"You will get, I think, the most serious and widely embraced philosophy that advances," he said.