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Critics say that measure fails to take into account government figures showing that men are almost twice as likely as women to work more than 40 hours a week, are much less likely to interrupt their work histories to have or raise children, and have other differences in labor market participation, including concentrations in higher-paying fields.

Indeed, the White House’s explanation for its own pay gap echoes such reasons, often cited by companies being sued over pay discrimination in the manner the administration wants to make easier.

Mr. Obama made the executive moves a day before the Senate was slated to vote on the Paycheck Fairness Act, which would require all employers to provide data on their pay breakdowns along gender lines. The act is unlikely to survive a filibuster, with Republicans and many business and retail groups arguing that the proposal would make it far too easy to sue companies and create a legal morass.

Republicans said Mr. Obama’s orders were election-year efforts to revive the “war on women” message that served the president’s 2012 campaign so well.

“All of us support equal pay for equal work. Let’s put the politics aside, and let’s get to work to see how we can make sure if there are problems with the law being implemented that we can address that,” said House Majority Leader Eric Cantor, Virginia Republican.

Although the open discussion of salaries may create headaches for employers, it could lead companies to be more mindful of their pay scales and to avoid inadvertent discrimination against women, said Deborah Thompson Eisenberg, associate professor of law and director of the Center for Dispute Resolution at the University of Maryland.

“If employers know they have to report what people in similar jobs are making and do that based on sex and race, then employers are more likely to be mindful about how they’re setting salaries,” she said.