(CNN) The Trump administration's approach to its latest asylum policy will encourage more people to cross the border illegally, the head of the Border Patrol's union told CNN on Friday, warning that officials are "opening up a Pandora's box."

The policy, which officials have said would begin on Friday, would send some asylum seekers back across the border to Mexico while their cases are pending in US immigration courts.

"This is attacking the legal process, because it's discouraging people from following the law," National Border Patrol Council President Brandon Judd said.

"We are incentivizing illegal immigration and punishing legal immigration."

It's rare for the president of the Border Patrol union -- who supported Trump on the campaign trail and recently stood beside him in Washington to help make the case for a border wall -- to criticize the administration's immigration policies.

Judd said he's speaking out because he's concerned the new policy will put more stress on Border Patrol agents.

"I do not see this as criticism of the President at all. I (am) critical that we are opening up a Pandora's box," he said.

"I'm raising these concerns because in essence what we are doing is punishing people who are trying to follow the laws and rewarding people who cross illegally."

Judd's comments that migrants will now be more likely to cross the border illegally echo concerns that immigrant rights advocates have raised about the new policy -- and about other efforts by the administration to limit how quickly cases are processed at ports of entry.

National Border Patrol Council President Brandon Judd told CNN the administration's latest asylum policy will encourage illegal immigration.

Immigrant rights advocates were quick to condemn the news that the new asylum policy would be implemented this week. And the measure, like other immigration policy changes by the Trump administration, is likely to face a swift challenge in court.

Administration officials say the new policy "will help restore a safe and orderly immigration process, decrease the number of those taking advantage of the immigration system, and the ability of smugglers and traffickers to prey on vulnerable populations, and reduce threats to life, national security, and public safety, while ensuring that vulnerable populations receive the protections they need."

An administration source told CNN on Thursday that the new policy would go into effect Friday at the legal border crossing with Tijuana, Mexico.

Mexican officials said Friday afternoon that they'd been informed by the US Embassy that 20 Central American migrants would be returned to Mexico through the San Ysidro Port of Entry "in the next few hours."

But there are still many unanswered questions about how the policy will work -- and what will happen next.

This isn't the first time Judd has criticized the administration. Last year, after officials deployed National Guard troops to the border, he called that effort a "colossal waste."

The Border Patrol union chief told CNN on Friday that the new policy won't be effective as long as migrants can still cross the border illegally and seek asylum.

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But that hasn't stopped the administration from making other changes to asylum policy, such as the measures going into effect Friday.

"If (the new policy) would have been rolled out to where every single person that claims asylum gets sent back to Mexico, I would have applauded this," Judd said.

But now, Judd said, since only migrants crossing at ports of entry will be subject to the new policy, they'll have little incentive to go that route.

"Would you rather be in Mexico or the US pending your court appearance? Most people would rather be in the US," Judd said. "It's a safer country."