The court on a 5-4 vote granted a request by a group of Republican state attorneys general to put on hold a judge's decision invalidating the emergency public health order known as Title 42 while it considered whether they could intervene to challenge the ruling.
The states had argued lifting the policy could lead to an increase in already-record border crossings. The court said it would hear arguments over the policy in its February session. A ruling is expected by the end of June.
"It breaks my heart that we have to keep waiting," Miguel Colmenares, a Venezuelan migrant in the Mexican border city of Tijuana, said on hearing about the court's decision.
"I don't know what I'm going to do, I haven't got any money and my family's waiting for me," the 27-year-old said.