R.J. Reynolds and other tobacco companies sought the high court’s intervention to keep the ban from taking effect by Dec. 21.
The administration had wanted a court order that would have allowed the program to take effect even as court challenges proceed.
The high court on Monday rejected GOP state chair Kelli Ward's request to halt the turnover of records while a lawsuit proceeds.
The high court is weighing an emergency appeal from Trump asking it to overturn a lower court ruling.
The building, closed in 2020 because of the coronavirus pandemic, remains off-limits to the public.
The 51-year-old Jackson is the court’s 116th justice and she took the place of the justice she once worked for.
The court’s ruling could complicate the administration’s plans to combat climate change.
President Biden says people should be peaceful when protesting the Supreme Court opinion that would allow states to ban abortion.
The ruling is the latest in a line of decisions from the Supreme Court that have favored religion-based discrimination claims.
The court is expected to rule on the case before its term ends in late June or early July.