Trump said on Twitter on July 26 that the USA government "won't acknowledge or enable transgender people to serve in any way" in the military, an inversion of Pentagon approach that the claim said was made without counseling senior military authorities.
Minter's group was joined by GLBTQ Legal Advocates & Defenders.
The service members suing the president are three US Army soldiers, one US Air Force airman and one member of the US Coast Guard who are on active duty.
A spokesman for the Defense Department declined to comment on the lawsuit, saying only that they were working with the White House to develop a written policy.
In the wake of Trump's ban tweet, Dunford issued a letter explaining the policy would not be changed until the White House issued additional "guidance", leaving an Obama administration policy that allows transgender people to openly serve in effect, for now.
"Execution of the President's directive will result in an end to service by openly transgender service members and has already resulted in immediate, concrete injury to Plaintiffs by unsettling and destabilizing plaintiffs' reasonable expectation of continued service", the suit states.
July 26, the president announced in a series of tweets that he would reverse President Barack Obama's previous policy on transgender servicemembers, stating "the United States Government will not accept or allow transgender individuals to serve in any capacity in the U.S. Military".
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"My experience has been positive and I am prouder than ever to continue to serve", one of the plaintiffs said in a statement released by her lawyers. "The military has been my life, but now I'm anxious about my family's future".
Robin Rayne Nelson/ZUMA Press/NewscomIt's still not clear how or even really if the military's transgender ban will proceed, but two legal organizations are nevertheless suing to try to stop it.
Former Defense Secretary Ash Carter ordered all branches of the military to draw up new policies that would allow for transgender recruits and transgender medical care within the military. So far, the Pentagon has not issued any official directive, as it has not yet received guidance from the White House.
The suit names Trump as a defendant, along with several top military officials, including Defense Secretary James Mattis and Joint Chiefs of Staff Chairman Joseph Dunford.
The Times reports other rights groups such as Lambda, Outserve, and the ACLU are also prepared to file lawsuits, but are holding off until the Trump administration actually takes steps towards implementing the ban.
Wednesday's lawsuit posits that Trump's tweet announcing the ban are a violation of the due process and equal protection clauses of the Bill of Rights.