On Friday Solicitor General Noel Francisco filed petitions, requesting Supreme Court justices to consider the issue in three separate cases, CNN reported.
The cases are still under review in lower courts, but the Trump administration is moving to challenge decisions from district courts across the country that have been able to block Trump's policy from going into effect.
Judges in federal courts in three jurisdictions, Washington state, California, and Washington, D.C., have refused to lift injunctions against Trump's ban, the BBC reported.
The policy was introduced in July 2017 by Trump on Twitter, followed by an official statement from U.S. Secretary of Defense James Mattis.
The Department of Defense had said individuals who have gender dysphoria could not serve in the military, with some exceptions.
Trump defended the decision in 2017, citing "tremendous medical costs and disruption."
The administration said on Friday it seeks "immediate review" of the constitutional challenges to the ban.
"And absent this Court's prompt intervention, it is unlikely that the military will be able to implement its new policy any time soon," the administration said.
Between 4,000 and 10,000 U.S. active-duty and reserve service members are transgender, and were allowed to serve in the military following a policy change under the Obama administration.
Trump has been critical of decisions by the United States Court of Appeals for the Ninth Circuit and districts in which it has jurisdiction.
Trump last week described Federal District Court Judge Jon Tigar, who put a temporary hold on the administration's plan for refusing to consider asylum applications from immigrants who cross the border illegally, as an "Obama judge."
This article has been updated to correct who appointed Roberts.