WASHINGTON — Transgender people can continue to serve in the military for now, Pentagon leaders said on Thursday, scrambling to clarify the confusion surrounding President Trump’s abrupt announcement a day earlier that transgender people would no longer be accepted or allowed in uniform.

In a letter to the military service chiefs, Gen. Joseph F. Dunford Jr., the chairman of the Joint Chiefs of Staff, said that the policy on who is allowed to serve would not change until the White House sends the Defense Department new rules and the secretary of defense issues new guidelines.

“In the meantime, we will continue to treat all of our personnel with respect,” General Dunford said in the letter.

Dana White, the chief Pentagon spokeswoman, said the Defense Department would provide detailed guidance in the “near future” on how Mr. Trump’s tweets will be turned into policy.