The American Civil Liberties Union says it appears unlikely the US government will meet a court-ordered Tuesday deadline to reunite 102 immigrant children under the age of five who separated from their parents at the US border.

US Judge Dana Sabraw in San Diego last month ordered the government to reunite more than 2,000 children who were separated from their parents under US President Donald Trump's "zero tolerance" policy that began in early May.

Sabraw set a deadline for children under five to be reunited by July 10, and all children by July 26.

The ACLU, which brought the lawsuit that led to Sabraw's order, said in a Sunday statement that the administration had provided them with a list of the 102 children under the age of five who have been separated.

But the organisation said it appeared "likely that less than half" of these children would be reunited by July 10.

"These kids have already suffered so much because of this policy, and every extra day apart just adds to that pain," Lee Gelernt, an ACLU attorney, said in a statement.

Gelernt said on Monday that the organisation was basing its allegation on conversations over the weekend with the government attorneys.

A government official who spoke on condition of anonymity said on Monday that the Trump administration has worked to reunite families with the shared goal of ensuring the safety of the children.

"The results of that work have been highly encouraging, and the Department of Justice is eager to present its progress to the court on Monday and to chart a path forward to safely reunifying other families expeditiously."

The government has said it may not meet the deadlines because of measures to ensure parentage and to determine the fitness of the parents. It also said it may not be able to locate some parents who were released from detention.

The government said it has dispatched teams to swab the cheeks of children and adults in its detention to test DNA to establish family connections, which the government has said is quicker than assembling documents such as birth certificates.