Last summer the administration had separated more than 2,500 children from their families before global outrage forced Trump to halt the practice and a judge ordered them reunited.
The lawsuit, on behalf of 11 asylum seekers from Central America and legal advocacy groups, says the Trump administration is violating USA law by failing to adequately evaluate the dangers that migrants face in Mexico.
The border slowdowns have occurred after Trump late last month threatened to close the frontier if Mexico did not halt a surge in undocumented migrants reaching the United States. And border agents say they're encountering more "fake families" among the growing number of Central American migrants crossing the border.
Vice President Mike Pence plans to visit the US Border Patrol Station in Nogales, Ariz., on Thursday, where he will be briefed by Customs and Border Protection agents and tour the border wall, according to a White House official.
They also are looking at trying to curtail the remittances immigrants send back home, looking to erase some of the economic incentive that draws them to the US, the official told reporters Tuesday, laying out a sweeping agenda for acting Homeland Security Secretary Kevin McAleenan, who is slated to start the job Wednesday.
At a Senate Homeland Security Committee meeting on border issues, child welfare and border officials warned there wasn't room or capability to start separating children on a large scale again. President Obama separated children.More news: This massive python just broke a record in the Florida Everglades
The Department of Homeland Security said last week that it planned to expand the programme.
To date, more than 700 people, including families, have been returned to Tijuana, and almost 200 more to Mexicali, according to a Mexican immigration official.
The president called on House Democrats to change the loopholes, which allow unsafe people to get into the U.S.
Speaking to Fox News on Monday, White House spokesman Hogan Gidley said: "It's time to do things a little differently". It was not immediately clear what would happen to those asylum-seekers when they come back to the US for their court dates.
Justice Department attorney Scott Stewart said at the March hearing there was a process to protect immigrants who could face harm in Mexico. The U.S.is also required to allow named plaintiffs of the lawsuit, who were returned to Tijuana, to enter the country within two days after the order goes into effect. As a result, "kids ended up kind of piling up in Border Patrol lockups, which are no places for children".
With the number of undocumented migrants crossing the border to enter the United States at its highest level in more than a decade, the president is desperately seeking to fulfil his signature campaign pledge to reduce unauthorized immigration into the US.