The announcement from the Supreme Court on Tuesday was a setback for President Donald Trump, who has ordered National Guard forces to support operations against migrants.
A federal district judge, April Perry, has already blocked the order to deploy forces in Chicago, Illinois, among other places. An appeals court chose not to oppose the federal judge's decision in October.
The Trump administration then chose to turn to the Supreme Court for a so-called urgent request to have the verdict overturned. Only two months later did the Supreme Court judge respond by not addressing the request, which means that the previous verdict stands.
The decision in Washington is not final, as there may be other avenues for the Trump administration to try to get the Supreme Court to address the issue. But Tuesday's decision means that such attempts are postponed to the future and is a political setback.
Soldiers primarily from the Texas National Guard have previously been ordered to Chicago to maintain law and order, according to Trump. Chicago's mayor and Illinois governor, both Democrats, have described the move as both dangerous and illegal.
