President Barack Obama signed an executive order prohibiting federal contractors from retaliating against employees for disclosing pay levels to co-workers and attacked Republicans for opposing broader legislation that would make the practice illegal for companies nationwide, according to the Associated Press.

Republicans said pay discrimination was already illegal and predicted the Democrat-supported Paycheck Fairness Act would prompt frivolous lawsuits and discourage companies from hiring, the AP reported.

The Democratic-led Senate is set to hold a procedural vote on the measure on Wednesday but even if the legislation clears that chamber, the Republican-dominated House of Representatives appears likely to oppose it, according to the AP.

The dispute underscored the importance that both parties place on women voters in an election year where Democrats fear losing control of the Senate and Republicans are seeking to defend their dominance in the House of Representatives, the AP reported.

"I don't know why you would resist the idea that women should be paid the same as men, and then deny that that's not always happening out there," Obama said at the White House at an East Room event filled with women, according to the AP.

"If Republicans in Congress want to prove me wrong, if they want to show that they, in fact, do care about women being paid the same as men, then show me. They can start tomorrow. They can join us in this, the 21st century, and vote yes on the Paycheck Fairness Act," President Obama added.

Obama cited U.S. Census data that show the average full-time female worker earned 77 cents for every dollar a man earns, according to the AP. The U.S. Department of Labor says the gap is tighter, with women in full-time jobs earning 81 cents for every dollar men earn.

Critics, including the U.S. Chamber of Commerce, a business lobby group, say both figures are misleading and added that other factors also affect the data, such as types of jobs worked by women, hours worked, and college majors, which affect whether people get higher- or lower-paying jobs, the AP reported.