A US judge has ordered that migrant children and their parents who were separated when they crossed into the US should be reunited within 30 days.
The judge issued the injunction in a case stemming from the administration's "zero-tolerance" immigration policy.
Meanwhile the policy of breaking up families at the Mexico border is being challenged by 17 US states.
Democratic attorneys general from states including Washington, New York and California launched the lawsuit.
More than 2,300 migrant children have been separated from their parents since early May under the Trump administration's controversial policy, which seeks to criminally prosecute anyone crossing the border illegally.
What did the judge say?
Tuesday's preliminary injunction, issued by a federal judge in San Diego, California, orders the government to reunite parents with their children aged under five within 14 days, and with older ones within 30 days.
The nationwide injunction was issued as part of a case filed by the American Civil Liberties Union (ACLU) on behalf of a mother who was split from her six-year-old daughter after arriving in the US last year.
Judge Dana Sabraw criticised "responses to address a chaotic circumstance of the government's own making".
Court papers filed by the ACLU contained accounts from other parents unable to locate their children after they were separated at the border.
Hasn't Trump already backtracked on separations?
Last week President Trump issued an executive order promising to "keep families together" in migrant detention centres.
It urged officials to expedite cases involving families. "We don't like to see families separated," Mr Trump said.
The order was widely seen as the reversal of a policy that had drawn widespread domestic and international condemnation.
On Monday US border security chief Kevin McAleenan said he had halted criminal prosecutions of migrants who illegally enter the country with children, following Mr Trump's announcement.
However critics have said the order is vague, and does not specify when and how those already split up would be brought back together.
Why are the states challenging the policy?
The lawsuit by the 17 states argues that the order does not prevent the policy being used again in the future. Neither, they note, does it say anything about reuniting families that have been separated.
They call the policy "an affront" to the states' interests in maintaining standards of care for children and preserving parent-child relationships.
New Jersey Attorney General Gurbir Grewal callled it "cruel, plain and simple" and accused the administration of "issuing new, contradictory policies" every day.
New York Attorney General Barbara Underwood said the administration was causing "causing unfathomable trauma" and that migrant children held in New York City had to be treated for depression and suicidal behaviour.
The lawsuit was filed with the US District Court in Seattle, Washington, on Tuesday.
The states involved are Massachusetts, Washington, New York, California, Delaware, Iowa, Illinois, Maryland, Minnesota, New Jersey, New Mexico, North Carolina, Oregon, Pennsylvania, Rhode Island, Vermont and Virginia plus the District of Columbia.
The lawsuit is similar to the case against the Trump administration's travel ban, which was initially blocked by Hawaii until the Supreme Court reversed the ruling on Tuesday morning.
What are officials saying?
Speaking in Brazil on Tuesday, US Vice-President Mike Pence warned undocumented immigrants not to "risk the lives of your children" by trying to enter the US illegally.
He said he had a message "straight from my heart" for those planning a journey to America: "If you can't come legally, don't come at all."
Also on Tuesday, the US health department's Office of Refugee Resettlement (ORR) confirmed that 2,047 migrant children were currently in the care of the agency.
The children have been sent to holding cells, converted warehouses, desert tents or foster care around the US.
ORR director Scott Lloyd refused to say whether the agency was still receiving migrant children who had been separated from their families.
https://www.bbc.com/news/world-us-canada-44622596