A majority of migrant children age five and under who were detained under the US immigration "zero-tolerance" policy have been reunited with their families.

Officials say 57 of the 103 children separated at the US-Mexico border were returned to parents as of Thursday.

But 46 children were ineligible for reunification, including some who's parents had already been deported.

Another 2,000 to 3,000 migrant children ages five to 17 must be reunited by 26 July, a US judge has ordered.

"As of this morning, the initial reunifications were completed. Throughout the reunification process our goal has been the well-being of the children and returning them to a safe environment," Health and Human Services Secretary Alex Azar, Homeland Security Secretary Kirstjen Nielsen and Attorney General Jeff Sessions said in a joint statement on Thursday.

"Of course, there remains a tremendous amount of hard work and similar obstacles facing our teams in reuniting the remaining families. The Trump administration does not approach this mission lightly, and we intend to continue our good faith efforts to reunify families."

The announcement comes two days after a court-ordered deadline to return the youngest of the children.

Officials said on Thursday that 22 children were unable be reunited with the adults that brought them illegally across the US border due to safety concerns.

Other children were determined to be ineligible to be returned to their parents for reasons including:

11 adults were found to have serious criminal histories

Seven were determined not to be the child's parent

One adult had a communicable disease

One adult allegedly abused a child while another planned to house the child with someone who had been charged with child abuse
Another 24 children were not eligible because parents were in custody for other criminal offences, officials were unable to locate them or they had already been deported back to their country of origin.

When asked about the deported parents in a conference call with reporters, federal officials said they are under "no obligation to bring people who have no lawful status in this country back into this country for reunification".

"These individuals had the opportunity to take the child with them when they were removed in the first place," said Matthew Albence, an official with Immigration and Customs Enforcement (ICE).

The parents are now being contacted through their embassies, he said, and will be given the option of having their children sent back to them.

The heavily-criticised policy of dividing children from adults crossing the border was suspended by US President Donald Trump last month after a fierce backlash.

Nearly 3,000 children were swept up under the "zero-tolerance policy" and the majority have yet to be reunited with their families.

The federal government has until 26 July to return the remaining children.