WASHINGTON—The Trump administration can deny asylum to Central Americans who cross through to the U.S., the Supreme Court said Wednesday, giving new life to White House efforts to deter a flood of immigrants seeking refuge at the southern border.

The court’s action, which came in a brief written order, effectively set interim rules that allow the administration to enforce its asylum restrictions while legal challenges to the policy continue, a process that could last many months. The high court’s order stayed the effect of...