The White House on Tuesday rejected calls to set aside a specific number of slots for LGBT Syrian refugees, but added that it would prioritize such cases.

White Hose Press Secretary Josh Earnest said that the Obama administration would not set aside 500 slots for LGBT people seeking asylum in the United States from Syria. Instead, Earnest said, the administration would prioritize the cases of individuals “deemed to be the most vulnerable.”

Earnest made his comments in response to a question on the subject from Washington Blade reporter Chris Johnson.

“There are no quotas that are set aside, but the process that we have implemented does prioritize the cases of those who have been subjected to torture, including like the torture that you described, or might have been singled out for their status as a minority, whether that’s a racial minority or an ethnic minority or a religious minority, or even somebody – an LGBT person,” Earnest said.

The Organization for Refuge, Asylum & Migration (ORAM) is among the groups calling for the set aside. A petition it launched gathered nearly 35,000 signatures.

“Living under a constant threat of being thrown from the top of a building or beheaded simply because of your sexual orientation or gender identity is about as extreme a form of persecution as you can image,” ORAM Executive Director Neil Grungras told the Blade. “Escaping that threat only to live in constant fear of being killed by other refugees or locals is too much for any human to bear.”