WASHINGTON — After months on the defensive over his health law, a more combative President Barack Obama has emerged to fight about gender politics, leading to an election-year competition with Republicans for support from women.

No single group will be more important to Democrats’ fortunes, say White House advisers, than unmarried women, who are likely to go Democratic — if they vote, and that’s far from certain when trust in Washington is low.

The president is trying to convince women that Democrats are more concerned about improving their financial standing in difficult economic times, and he charges Republicans with standing in the way. “Republicans in Congress have been gumming up the works,” he said at White House event on equal pay.

“This isn’t just about treating women fairly. This is about Republicans seemingly opposing any efforts to even the playing field for working families,” Obama said.

Republicans say they have learned important lessons from previous elections where women helped put Obama and other Democrats in office. This year, the GOP is promising an aggressive counterattack.

The Republican National Committee plans to a new initiative, “14 in ’14,” to recruit and train women under age 40 to help spread the party’s message in the final 14 weeks of the campaign.

Representatives from all the party committees — the RNC and those supporting GOP candidates for Senate, House, governors and state legislators — meet regularly to plan strategy and advise candidates.

They are encouraging candidates to include their wives and daughters in campaign ads, have women at their events and build a Facebook-like internal database of women willing to campaign on their behalf.

Responding to Obama’s equal pay event, Republicans cried hypocrisy and pointed out that women on average make less than men on the White House staff. When the Senate voted on an equal pay measure the next day, every Republican voted no and said the law already protects women from being paid less than men.

The Republican Party committees are circulating figures showing that poverty among women has risen during Obama’s time in office, while women’s average wages have dropped.

They say they are targeting older women, who are more likely to vote Republican than younger women, in part by highlighting cuts to Medicare Advantage plans that the Obama administration proposed and then reversed under pressure. They say they will continue to press the case that the health law has increased costs for some people and affected their health care plans.

“It feels to us like the White House and Democrats are making decisions on legislation and messaging priorities based on the fact that they have to talk about anything but Obamacare to appeal to their depressed base,” said Republican National Committee spokeswoman Kirsten Kukowski.

Obama cites the Affordable Care Act as an example of improved gender equality. “Tens of millions of women are now guaranteed free preventive care like mammograms and contraceptive care, and the days when you could be charged more just for being a woman are over for good,” he said in his weekly address this weekend.

Obama has promoted women’s economic issues at White House events and in recent trips to Florida and Michigan, tightly contested states.

He embraced six original Rosie the Riveters — women who took on traditionally male jobs during World War II — on a recent White House visit, and holds them up as an example of equal pay for equal work. He held the first White House event on combating campus sexual assault.

The White House plans a June summit on economic issues facing working families, with a series of regional meetings leading up to it. Administration officials and Cabinet members plan to host business school deans at the White House to talk about workplace policies that could even the playing field for women.

Aides say the president will focus more in the coming weeks on workplace flexibility and the need for child care, including universal prekindergarten.

Neil Newhouse, pollster for Mitt Romney’s Republican presidential campaign in 2012, helps conduct nonpartisan focus groups of moms who shop at Walmart. He said the Democrats’ performance this year depends entirely on their ability to turn out critical groups of voters, including women, who sided with Obama in 2012.

“All the work we’ve done with Walmart moms is that these women feel abandoned by Washington, abandoned by their political leaders. This eight-year plus recession has drained them emotionally and financially, and they don’t look to Washington any more for help,” Newhouse said. “The voters who are most motivated right now to vote in the midterm are Republicans and conservatives. But that’s seven months away, several lifetimes in politics. Anything can happen.”