The order — which may never become administration policy, depending on internal deliberations — would also free some private companies from being forced to provide contraceptive coverage as part of the health plans they offer employees. And it would open the door for tax-exempt entities to speak out "on moral or political issues from a religious perspective" without fear of losing favored tax status.
"We do not have plans to sign anything at this time but will let you know when we have any updates," said Sarah Huckabee Sanders, a White House spokesperson.
"President Donald J. Trump is determined to protect the rights of all Americans, including the LGBTQ community," the White House said in a statement Tuesday morning. "President Trump continues to be respectful and supportive of LGBTQ rights, just as he was throughout the election."
A copy of the draft document was provided to ABC News by a government official who was authorized to review it but was not authorized to release it publicly. The four-page draft executive order is titled "Establishing a Government-Wide Initiative to Respect Religious Freedom."
"If anything in this document were to become federal law, it would be a national license to discriminate, and it would endanger LGBTQ people and their families," said Sarah Kate Ellis, GLAAD's president and CEO.
The draft order reads that it would be the policy of the administration that "Americans and their religious organizations will not be coerced by the federal government into participating in activities that violate their conscience and will remain free to express their viewpoints without suffering adverse treatment from the federal government."
"I think this is going to be addressed," Perkins said. He did not respond to requests for comment on Wednesday.
Religious groups have argued that Obama-era policies have curtailed their freedoms by forcing them to provide services that conflict with their beliefs. Mallory Quigley, the communications director for the socially conservative Susan B. Anthony List, said an order protecting religious freedoms is critical for the new president to deliver on promises made to his conservative base.
"It is an expectation of the pro-life movement that the Trump administration would provide relief for Little Sisters of the Poor and others who have had their conscience rights violated by Obamacare," Quigley said. "This would certainly be in keeping with the priorities that the administration has already laid out."
While not rescinding any previous executive orders, the proposed order could free companies and individuals that do business with the federal government to decline to work with gay and lesbian couples on adoptions and other services.
The draft order states that the federal government "shall not discriminate or take any adverse action against a religious organization" providing adoption or child-welfare services if the organization "declines to provide, facilitate or refer such service due to a conflict with the organization's religious beliefs."
After being provided a copy of the draft by ABC News for review, a spokesman for a prominent gay-rights group said the order could permit federal employees and contractors to refuse a range of services to people based on their sexual orientation or gender identification.
Chad Griffin, the president of the Human Rights Campaign, called the draft "sweeping and dangerous."
Also, the proposed order would exempt "all persons and religious organizations" from providing health care options that include contraceptive coverage, as required under the Affordable Care Act, if they "object to complying with the mandate for religious or moral reasons."
The order would expand the definition of a religious organization to include "closely held for-profit corporations, operated for a religious purpose, even if its purpose is not exclusively religious."
That would apply to companies like Hobby Lobby, which brought a landmark case against the Obama administration challenging the requirement that employer-provided health care include contraceptive coverage.
The order would ensure tax-exempt status for religious organizations if they speak out on beliefs opposing gay marriage, extramarital sex, abortion rights and rights for transgender individuals.
That would roll back aspects of the Johnson Amendment, a 1954 law prohibiting tax-exempt organizations from endorsing or opposing political candidates. Trump promised repeal of the amendment as a candidate, though congressional action would be necessary for that to occur.
The order would establish a working group in the Justice Department to "ensure that the religious freedom of persons and religious organizations is protected throughout the United States" and take "appropriate action."