The county on the Mexican border said the decision to end the program last October left the county struggling to help some of the thousands of people who effectively have been stranded in the county because they no longer are receiving federal help in reaching relatives or others in other part of the country who could house them.
The federal lawsuit called the move "arbitrary and capricious."
Administration officials did not immediately respond to messages seeking comment Wednesday night. They have said previously that they are under no legal obligation to provide travel assistance and that growing numbers of family arrivals prevent them from doing so any longer.
Families arriving at the border have long been released from U.S. custody and allowed to settle in this country with family or friends while their cases wound their way through the courts, a process that often takes years. The change in October was how quickly it happened.
But in recent months, the number of families crossing into the U.S. has climbed to record highs, pushing the system to what administration officials say is a breaking point.
Since Dec. 21, Immigration and Customs Enforcement has set free more than 125,000 people who came into the U.S. as families.
Customs and Border Protection is also overloaded, and instead of holding families for up to 72 hours before turning them over to ICE, it has started releasing them directly into the U.S., sometimes so quickly they haven't time to make travel arrangements. Families are given court dates, a head of household is often fitted with an ankle monitor, and they are dropped off at a charity-run shelter or bus station.
Relief organizations in some cities are struggling to feed and house the migrants and warning that a public health crisis is taking shape, especially with sick infants and children among the many immigrant families who need medical attention.
San Diego County recently opened a shuttered downtown courthouse slated for demolition to house up to 150 asylum seekers. A coalition of religious and civic groups that manages the shelter said it has helped more than 11,000 members of asylum-seeking families since authorities began large-scale releases in late October.
"The federal government's negligent approach to those seeking asylum is taking a huge toll on San Diego County taxpayers," Board of Supervisors Chairwoman Dianne Jacob tweeted. "The county has already spent over $1.3 million to address health and safety issues at the asylum shelter. That figure is ballooning by the day."
The lawsuit says it wants the restoration of the safe release program, including restoration of federal assistance in reaching their final destinations in the U.S.