WASHINGTON — The Trump administration has offered conflicting messages and no clear solutions for reuniting more than 2,300 migrant children who were separated from their parents at the U.S.-Mexico border under a policy that dictated all parents be charged and separated while awaiting a court hearing.

The executive order signed by President Donald Trump Wednesday ended family separation at the border, but was silent on reunifying already separated kids with their parents.

On Thursday afternoon, a spokesman for the Health and Human Services Department told NBC News that all separated kids currently in HHS custody would continue to follow the existing "sponsorship process" for minors, meaning they would be paired with relatives or foster parents, rather than the biological parents from whom they were separated at the border. HHS said it would continue to follow that process until it received further guidance from the Department of Homeland Security.

But later Thursday, another HHS spokesman updated the agency's position, saying "reunification is always the ultimate goal" — but didn't say that reunification would necessarily be with parents. Instead, the spokesman said only that HHS was focused on "reunifying minors with a relative or appropriate sponsor."

For now, parents who were intercepted by border agents prior to the executive order and have already been charged with crossing illegally are being held in the custody of U.S. marshals while their children are in the care of HHS at one of 100 centers across 15 states.

How to find a migrant child

The government may not have settled on what reunification means, but there is an existing method for these parents to reconnect with their children.

Adults who are intercepted entering the country illegally receive something called an "A file" number from DHS that designates their legal case. If they are accompanied by their children, the kids receive the same A file number.

If parents are separated from their children, however, the children receive different A file numbers, which can make it more complicated to pair parent and child in the future.

According to a U.S. official, there are A file numbers for the 2,300 separated kids.

The A file can be used by government agencies to track kids if they are sent by HHS to live with foster families, in government facilities or in private facilities run by government contractors.

Theoretically, after the migrant parents who were separated from their kids have their cases adjudicated, meaning after they are deported, jailed or released, they can use these A file numbers to locate their children or to arrange communication.

Immigrant children housed in a tent encampment under Trump administration's "zero tolerance" policy at the facility in Tornillo, Texas, on Tuesday. Mike Blake / Reuters

A parent who is behind bars, however, may find it very difficult to communicate with a child who is also in custody. A parent deported from the U.S. may find it hard to navigate the U.S. legal system or immigration bureaucracy from abroad, or just to complete a phone call.

And it may take months for families to be reunited, since a child's immigration case can move much slower than an adult's.

"You could easily end up in a situation where the gap between a parent's deportation and a child's deportation is years," said former Acting Immigration and Customs Enforcement Director John Sandweg.

Previously, when federal agents separated children from their parents it was usually because they believed the children's welfare was in danger.

Sandweg told NBC News earlier this week that some separations of migrant kids and parents may be permanent.

In response to Sandweg's comments, a spokeswoman for ICE explained how parents who are ordered to be deported have reunited with their children in the past on a case-by-case basis.

"A parent who is ordered removed may request that his or her minor child accompany them," said spokeswoman Liz Johnson. "If the parent chooses to have his or her children accompany him or her, ICE accommodates, to the extent practicable, the parent's efforts to make provisions for their children. As appropriate, ICE will work with the adult to have the child return to their country of citizenship with them."

"When parents are removed without their children, ICE, ORR (the Office of Refugee Resettlement), and the consulates work together to coordinate the return of a child and transfer of custody to the parent or foreign government upon arrival in country, in accordance with repatriation agreements between the U.S. and other countries," Johnson said.

But it remains unclear how ICE and HHS will work together to systematically unify more than 2,300 children.

For migrant families who are intercepted by U.S. border agents after Wednesday's executive order, the process will be different.

In the future, migrant parents who cross the border illegally with their children will still be prosecuted for illegal entry, but they will live with their kids in family detention run by U.S. Immigration and Customs Enforcement while awaiting their hearing.

The families may be detained for months on end because the Trump administration plans to file a request to change a federal court decision that limits the amount of time children can be detained with their parents to 20 days.