President Obama, resisting calls from several prominent faith leaders, will not include a new exemption for religiously affiliated government contractors when he issues an executive order Monday barring discrimination on the basis of sexual orientation and gender identity, the White House said Friday.

Obama announced last month that he would sign such an order after concluding that Congress was not going to act on a broader measure prohibiting discrimination based on sexual discrimination or gender identity by companies.

Since then, faith leaders have urged him to include an exemption for government contractors with a religious affiliation, such as some social service agencies.

White House officials said Friday that the new executive order would not include such an exception. But Obama will preserve an exemption put in place by former president George W. Bush that allows religiously affiliated contractors to favor employees of a certain religion in making hiring decisions.

Gay rights organizations have criticized that earlier exemption, and they celebrated news Friday that Obama would not be broadening it.

“With the strokes of a pen, the president will have a very real and immediate impact on the lives of millions of LGBT people across the country,” said Chad Griffin, president of the Human Rights Campaign, a gay rights group.

Michael Wear, a former Obama faith adviser who had organized a letter to Obama urging him to include a religious exemption, said he was gratified that Obama preserved the Bush exemption. But he said that because “faith-based contractors will not be completely exempt from the president’s executive order,” it will be important to provide “clarity” on what behavior is consistent with it.

“We risk opening up the doors for litigation that leaves both LGBT Americans and religious organizations uncertain and unprotected,” he wrote in a statement.

The order protecting lesbian, gay, bisexual and transgender people is the latest administration policy to become embroiled in a debate over religious rights. In a blow to Obama’s health-care law last month, the Supreme Court ruled that family-owned businesses do not have to offer contraceptive coverage that conflicts with the owners’ religious beliefs.