President Obama on Monday signed an executive order prohibiting federal contractors from discriminating on the basis of sexual orientation and gender identity, saying that, with the move, "our government will become a little bit fairer."

"America's federal contracts should not subsidize discrimination against the American people," Obama said during a ceremony at the White House.

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The president called on Congress to pass the Employment Non-Discrimination Act (ENDA), legislation that has passed the Senate and would extend employment discrimination protections to all LGBT workers in the private sector.

"I firmly believe that it’s time to address this injustice for every American," Obama said, urging gay rights activists to "keep putting pressure on Congress to pass federal legislation that resolves this problem once and for all."

But some gay and civil rights groups have abandoned ENDA over concerns stemming from the Supreme Court's Hobby Lobby decision. The organizations expressed concern that the religious exemption included in the Senate version of the bill could be exploited by employers to discriminate against LGBT individuals.

Those groups say that, if the law were interpreted as it was in the Hobby Lobby case, which allowed some privately held companies to opt out of paying for birth control coverage in their healthcare plans, hospitals, nursing homes, and universities could institutionalize discrimination.

The president's executive order signed Monday does not include any additional exemptions for religious entities, beyond one implemented during President George W. Bush's administration that allows religiously affiliated contractors to favor members of their faith when making hiring decisions.

It amends an executive order first issued by former President Lyndon Johnson, adding sexual orientation and gender identity to a list of protected categories including race, color, religion, sex, national origin, disability and age.

"We have an obligation to make sure the country we love remains a place, where no matter ... who you love, you can make it," Obama said.

Obama had for months resisted calls from gay rights groups to draft the order, with White House aides saying the president wanted Congress to pass legislation extending anti-discrimination protections to all American workers. But after passing the Senate in November, the anti-discrimination bill went nowhere in the Republican-controlled House.

“Shockingly enough, the House refused to act,” Obama said an LGBT gala in New York City earlier this month, noting Congress had been “considering legislation to protect LGBT workers for decades.”

Top Republicans, including Speaker John Boehner (R-Ohio), have called the bill redundant and warned it would cost jobs by creating frivolous litigation.

The president's aides said the move underscored how the president was willing to act despite congressional obstruction.

"Today's LGBT employment Executive Order demonstrates once again how a President can change lives for the better with the stroke of a pen," tweeted senior presidential adviser Dan Pfeiffer.

Anthony D. Romero, the executive director of the American Civil Liberties Union, called the order “one of the most important actions ever taken by a president to eradicate LGBT discrimination from America's workplaces.”

"While there remains much work still to do to achieve the goal of full civil rights protections for LGBT people, we must take time to celebrate the landmarks along the way, and this is a huge win,” he said.