(CNN) The Pentagon is compiling names of people who supported US military operations in Iraq so they can more easily receive waivers under the new executive order on immigration, Pentagon spokesman Capt. Jeff Davis said Monday.

Davis said the White House invited officials to submit the names over the weekend because "there is a recognition that this is an important group of people."

Earlier Monday, CNN reported the Pentagon was considering sending the White House a list of Iraqis that supported the US military in Iraq.

JFK airport detention

Without waivers, the problems these Iraqis may experience under the new policy were illustrated Saturday when two men were detained at John F. Kennedy International Airport, setting off a large protest.

Hameed Khalid Darweesh worked with the US government for 10 years after the United States invaded Iraq. Haider Sameer Abdulkaleq Alshawi had been granted a visa to join his wife, who worked for a US contractor in Iraq, and son, both of whom already live in the United States as refugees.

The two men are part of a class-action lawsuit that was the first legal challenge to Trump's executive order.

Help for Iraqis

Kirk Johnson, an advocate for Iraqis who served the US government, told CNN the US government has a moral obligation to make immigration easier for them.

"I would like the president of the United States to explain (the new policy) to the tens of thousands of Iraqis who have risked their lives," said Johnson, a former US Agency for International Development worker, founder of the List Project , which helps Iraqis resettle, and author of "To Be a Friend Is Fatal: The Fight to Save the Iraqis America Left Behind."

Over 100,000 of these Iraqis risked their lives for us during the war. They bled for our country. /4 — Kirk W. Johnson (@KirkWJohnson) January 29, 2017

He said because lives are at stake, action must be taken soon.

'The most documented refugees'

"This is not a time where kinks are to be worked out," he said. "This was a colossal -- sorry to say it -- a colossal middle finger to the service of tens of thousands of Iraqis and others who have done more for this country than most living, breathing Americans."

Those in airports had tickets ripped up in front of their faces. They were told that President Trump doesn't want them in America. /39 — Kirk W. Johnson (@KirkWJohnson) January 29, 2017

Johnson said the authors of Trump's executive order don't seem to understand that Iraqis who help the US military have been thoroughly examined.

"These interpreters that you're seeing stranded at JFK ... are the most documented refugees on the face of the planet," he said.

He said solders, aid workers and state department officials have vouched for their service.

"You don't get to ride around in Humvees with Marines unless you've been vetted," Johnson said. "So when I hear President Trump talk about how there hasn't been any vetting before, I don't know what world he's living in."