Two LGBTQ rights groups are suing President Trump over his plan to ban transgender people from serving in the U.S. military.

The National Center for Lesbian Rights (NCLR) and GLBTQ Legal Advocates & Defenders (GLAD) on Wednesday filed a lawsuit in the U.S. District Court for the District of Columbia on behalf of five transgender service members.

They claim the president's July tweets announcing plans to reverse the Department of Defense’s policy on transgender service members violates the Equal Protection component of the Due Process Clauses of the Fifth Amendment.

“The categorical exclusion of transgender people from military service lacks a rational basis, is arbitrary, and cannot be justified by sufficient federal interests,” the groups said in their complaint.

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The plaintiffs in the case, listed only as Jane Doe 1, 2, 3, 4 and 5, have nearly 60 years of combined service, according to the groups.

In making the announcement on Twitter in July, Trump said he had consulted with “generals and military experts” and decided the “United States Government will not accept or allow Transgender individuals to serve in any capacity in the U.S. Military.”

“Our military must be focused on decisive and overwhelming victory and cannot be burdened with the tremendous medical costs and disruption that transgender in the military would entail. Thank you,” he said in a second tweet.

Joint Chiefs of Staff Chairman Gen. Joseph Dunford issued a letter the next day indicating the policy would not be changed until the White House issued further "guidance."

“There will be no modifications to the current policy until the president’s direction has been received by the secretary of defense and the secretary has issued implementation guidance,” Dunford wrote.

The groups suing Trump, however, say their clients have already been harmed because they no longer have a reasonable expectation they can continue serving.

“Trump’s directive to exclude transgender people from military service has created a tidal wave of harms that have already been felt throughout our armed services,” Shannon Minter, a transgender legal expert and NCLR’s legal director, said in a statement.

“Transgender service members have been blindsided by this shift and are scrambling to deal with what it means for their futures and their families. The President’s mistreatment of these dedicated troops will serve only to weaken and demoralize our armed forces.”

The Palm Center released a report Wednesday that estimates it would cost $960 million, or $75,000 per person, to recruit and train replacements for the estimated 12,800 transgender troops serving in the armed forces.

The report points to research from the The Rand Corporation, a global policy think tank, which estimates the government would only save $8.4 million per year in the cost of medical care for transgender troops if the ban were put in place.

“If President Trump is truly concerned about the financial costs of transgender service his announced ban has it exactly backwards,” Aaron Belkin, the Palm Center’s director and co-author of the report, said in a statement . "American taxpayers should ask the president, who is proud of his business savvy, why he’s spending a dollar to buy a dime.”

- This story was updated at 1:48 p.m.