House Republican Conference Chair Liz Cheney (R-Wyo.) and fellow GOP House leaders hold a news conference at the Capitol on June 11. (Chip Somodevilla/Getty Images)

Rep. Liz Cheney, the top-ranking woman among House Republicans, said Wednesday that her party needs to do a better job of recruiting female candidates and winning the votes of women, after a crushing defeat for a GOP woman in a North Carolina runoff.

Cheney (Wyo.), chair of the House Republican Conference, was speaking one day after state Rep. Greg Murphy bested pediatrician Joan Perry to win the GOP nomination for a U.S. House seat in North Carolina.

Perry had received nearly $1 million in support from an outside group created to boost female Republican House candidates and was endorsed by all 13 female House Republicans.

“We have to work very hard as Republicans to convince more women to run for office, but also to convince more women to vote for us,” Cheney said at the Capitol.

The gender gap among both parties in the House, already wide after the 2016 election, expanded even further after the 2018 midterms, when Democrats sent a record 89 women to the House while the number of Republican women plummeted from 23 to 13. The disparity is evident in the leadership of both parties, with House Speaker Nancy Pelosi (Calif.) the top Democrat in the chamber.

At the presidential level, as well, Republicans trail among female voters. A Washington Post-ABC News poll released Sunday shows that in matchups against five potential Democratic challengers, President Trump receives between 38 percent and 42 percent support from women.

The primary in North Carolina’s 3rd Congressional District was viewed by many as a test of women’s standing in the Republican Party, particularly given the heavy involvement of Winning for Women Action Fund, a GOP super PAC that was created to back female Republican candidates in congressional races.

Among those backing Murphy in his winning bid were Reps. Mark Meadows (R-N.C.) and Jim Jordan (R-Ohio), the chairman and former chairman, respectively, of the conservative House Freedom Caucus.

House Minority Leader Kevin McCarthy (R-Calif.) on Wednesday sought to put a positive spin on Perry’s loss, noting that the North Carolina Republican received “a tremendous amount of support” and that she “was able to make a runoff having never run before.”

“This was a great improvement, and I look forward to seeing more women elected in this Republican new Congress,” he said.

But McCarthy also acknowledged that there remains some hesitance among the Republican Party base to support female or minority candidates.

“The biggest challenge ever for women and minorities are always within the primary,” he said.

Murphy will face former Greenville mayor Allen Thomas (D) as well as Libertarian and Constitution Party candidates in the Sept. 10 special election. But the district is a reliably Republican one — Trump won it by 23 percentage points in 2016 — meaning that with Perry’s loss, House Republicans are on track to welcome the 182nd white male lawmaker to their caucus’s ranks this fall.

Cheney said that “attracting women voters is crucial” and that one way for Republicans to make their case to them is to argue that Democrats are advancing “policies that are scary to all Americans, and particularly to women.”

“If you look at health care, for example, women are the ones that make the decisions primarily. The majority of health-care providers are women,” she said.

Cheney has been mulling a Senate run, a move that would further diminish the ranks of female House Republicans. She said Wednesday that she has not “made a decision yet in terms of what’s happening next.”

Another top House Republican woman, Rep. Susan Brooks (Ind.), has announced that she will not seek reelection next year. Brooks, who had backed Perry and is the National Republican Congressional Committee’s recruiting chair, on Wednesday dismissed the notion that the North Carolina race was a proxy battle between the House Freedom Caucus and House Republican women.

“Honestly, no, I don’t think Mark Meadows won that election for Dr. Murphy,” she said. “Similarly, I don’t think the women in Congress would have won that election for Dr. Perry. Do you see what I’m saying? To me, I feel strongly that it is the people at home, working in their districts and connecting with voters in their districts.”

Brooks said that the Republican Party as a whole needs to “do better at the local level” to recruit women to run for office, beginning with city council members and county commissioners, and “then we have to really do more to help them at the state level.”

Asked whether she is doing more in her own district to make sure a woman succeeds her when she retires next year, Brooks demurred.

“It is not about me replacing myself, or helping find — I’m obviously encouraging, I’m talking to women, I’m talking to men,” she said. “Once again, it has to do with the best fit at the time of the election and with that candidate, whether it’s a man or a woman, it’s gotta be the best person at that time.”