For now, Dunford has informed service members that 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 guidelines."
"In the meantime, we will continue to treat all of our personnel with respect," Dunford wrote in a memo to the military that was obtained by CNN. "As importantly, given the current fight and the challenges we face, we will all remain focused on accomplishing our assigned missions."
Army Chief of Staff Gen. Mark Milley said Thursday that, to date, he has not received "directives on implementation" for a ban and learned about the President's decision through the media.
"We will work through the implementation guidance when we get it and then we'll move from there," he added while speaking at the National Press Club.
Trump announced Wednesday that transgender individuals would no longer be allowed to enlist or serve in the military.
"After consultation with my Generals and military experts, please be advised that the United States Government will not accept or allow Transgender individuals to serve in any capacity in the U.S. Military," Trump said in a series of tweets. "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."
His tweets came less than a month into the six-month delay set by Defense Secretary James Mattis to review the US military's policy on transgender service members.
A US official told CNN that Mattis was consulted on Trump's plan to announce a ban, but Sen. John McCain said on Thursday that he was surprised by the announcement.
"I think they realize they made a mistake," the Arizona Republican said. "I think generally speaking, it's accepted you consult the secretary of defense before you make a decision that has to do with defending the nation. Mattis was going through a study that they'd done for six months, and he had just extended."
"I know what Mattis said, that he wanted to complete the study, and he was surprised," added McCain, who chairs the armed services committee.
But while Trump's tweet states that he consulted with his generals and military experts ahead of making the announcement, US defense officials have indicated that many of the top brass were caught off guard by the policy change.
One of the heads of the military branches was informed by a staffer of the President's tweets on transgender policy and had no idea it was coming, an official said.
Adding to the confusion is that Trump's decision came without a plan in place to implement it.
White House press secretary Sarah Huckabee Sanders did not have an answer Wednesday on what would happen to active transgender military members but said the White House and the Defense Department would work together "as implementation takes place and is done so lawfully."
But how those next steps would play out still remains unclear.
The Pentagon has asked the White House for a written directive spelling out its intentions and directions on transgender policy so the military can begin implementing guidance, according to a defense official with direct knowledge.
A major issue now is whether currently serving members will be discharged and whether they will receive an honorable discharge so they can continue to receive whatever medical and retiree benefits they are entitled to based on their years of service, a defense official said.
Democratic Rep. Steny Hoyer blasted Trump for keeping top military leaders in the dark during an interview with CNN's Kate Bolduan on Thursday.
"When I hear the chairman of the Joint Chiefs of Staff had no idea he was going to do this, it's another indication, the only reason it was done was to appeal to some House members and those who wanted to and offered an amendment to discriminate against those transgender members of the armed forces," Hoyer said.