The US' controversial "zero tolerance" immigration policy is not flying with airline companies operating in the US.

A Mexican airline announced on Friday it is offering seats to migrant children separated from their parents at the US southern border to fly back to their home countries "at no cost", while US carriers have asked the authorities not to use their flights to transport children of illegal crossers.

Ultra-low-cost airline Volaris said it is ready to fly children hit by the US policy on its pre-existing routes to reunite with their families.

"It is heartbreaking to see children separated from their parents and it is our mission to reunite them," Volaris said in a statement posted on Twitter.

"Families belong together and our commitment is to help them stay together to better build their future," it added, noting that it is willing to coordinate the logistics with the authorities of the "United States, Mexico and the countries where it operates in Central America."

Last year, Volaris transported more than 16.4 million passengers to over 65 destinations across Mexico, the United States, Guatemala, El Salvador, Nicaragua and Costa Rica.

Concerned families have yet to approach the airline to take advantage of the offer, the Los Angeles Times newspaper quoted Volaris spokesperson Ana Ambrosi as saying, adding that the carrier will use social media in the next weeks to spread the word.

The US immigration policy, introduced in April, criminally prosecutes immigrants who cross into the US illegally. It has since split up families with no proper documents, moving parents to federal jails pending trial, while placing children under the custody of US authorities.

A total of 2,342 minors have been removed from their parents' care in the past five weeks, authorities announced on Tuesday, triggering outrage and criticism and leading to widespread protests fueled by images of youngsters in cages and reports of child abuse at government-funded facilities.

President Donald Trump, a staunch backer of the policy, bowed to mounting pressure, and signed on Wednesday an executive order to detain families together. But the about-face didn't ease concerns with questions arising over the vague language of the order which greenlights separation if detention with the legal custodian "would pose a risk to the child's welfare", and the fate of children after being detained with their parents for 20 days (The current maximum period for minors to be held in custody in the US).

US airlines have also taken the decision to steer away from the storm, asking the federal government not to use their flights to transport migrant children away from their parents – announcements the US Department of Homeland Security (DHS) described as "unfortunate."

Earlier this week, Texas-based American Airlines said it was not sure if the federal government flied any migrant children aboard its planes, but said it would be "extremely disappointed to learn that this is the case."

"The family separation process that has been widely publicized is not at all aligned with the values of American Airlines — we bring families together, not apart," the carrier said.

United, Frontier and Southwest Airlines also issued similar announcements saying they will not be involved in the process of separating families.

"It’s unfortunate that @AmericanAir , @united, and @FlyFrontier no longer want to partner with the brave men and women of DHS to protect the traveling public, combat human trafficking, and to swiftly reunite unaccompanied illegal immigrant children with their families," DHS spokesperson Tyler Houlton tweeted in response.

(With input from Reuters)

(Cover: People take part in a protest against US immigration policies outside the US embassy in Mexico City, Mexico, June 21, 2018. /VCG Photo)