A week after President Trump tweeted a proposed ban on transgender military service, the Defense Department says it’s holding conversations with White House staff on the issue, which would affect thousands of current service members if a prohibition were enacted.

But Trump himself, since his tweets, has provided no explanation, to the Pentagon or the public, of how his policy would work, how service members would be identified and discharged, or when it would take effect.

“We are now in the process of waiting for that to be formally articulated in a policy memo,” Navy Capt. Joel Davis, a Defense Department spokesman, told reporters Monday. “We’re awaiting a formal order from the commander-in-chief to proceed.”

The department, he said, has heard nothing from the president since his tweets last Wednesday. Pentagon officials, Davis said, “have conversations back and forth all the time with the White House on a variety of issues, and those conversations are starting to happen on the (transgender) issue.”

Army Lt. Col. Paul Haverstock, another spokesman, said by email Tuesday that Pentagon leaders “will provide detailed guidance to the (Defense) department in the near future for how this policy change will be implemented.” He provided no timetable, but said the armed forces would adhere to their principle of “ensuring all service members are treated with respect.”

President Barack Obama’s administration lifted a prohibition on openly transgender service members in July 2016 after a study it had commissioned forecast minimal disruption or financial costs to the military. The study, by the Rand Corp., estimated the number of transgender service members at between 1,320 and 6,630, out of a total of 1.3 million in the armed forces, while the Williams Institute at UCLA Law School has estimated the number at 15,000.

In announcing the ban, Trump tweeted that he was acting only “after consultation with my Generals and military experts.” But the announcement caught the nation’s military commanders by surprise, and they have not shown any eagerness to comply.

On Tuesday, the Coast Guard’s leader, Adm. Paul Zukunft, said he would not abandon the 13 Coast Guard members who have identified themselves as transgender, according to the Military.com website. The Coast Guard is a military agency but is part of the Department of Homeland Security, not the Defense Department, and it’s not clear whether it would be affected by Trump’s order.

Zukunft, describing his conversation with one transgender officer, Lt. Taylor Miller, said he told her, “I will not turn my back. We have made an investment in you, and you have made an investment in the Coast Guard, and I will not break faith.”

Also on Tuesday, Palm Center, a gay-rights nonprofit in San Francisco, released a statement by 56 retired U.S. generals and admirals saying a transgender ban would be both unfair and harmful to the military.

“Patriotic transgender Americans who are serving — and who want to serve — must not be dismissed, deprived of medically necessary health care, or forced to compromise their integrity or hide their identity,” the statement said.

Although Trump, as commander-in-chief, can issue binding orders to the military services, his tweets don’t appear to be specific or detailed enough to compel immediate action, said Eugene Fidell, a military lawyer who teaches courses on the subject at Yale Law School.

Military leaders are not “being in any degree insubordinate by waiting for the White House to put some flesh on the bones of the tweets,” Fidell said in a blog post Monday. Once that happens, he said, the armed forces would issue guidelines — a process “likely to take weeks if not months” — before discharging transgender personnel.

Advocacy groups, including the National Center for Lesbian Rights in San Francisco, have promised to file lawsuits arguing that a transgender ban would violate the constitutional guarantee of equal protection of the laws.

One question the guidelines will have to address is whether transgender should be defined narrowly, applying only to service members under medical treatment, or more broadly to include self-identification. The California prison system, in a lawsuit that led to an inmate’s sex-reassignment surgery, adopted a broad definition in April covering inmates whose “sense of identification” was different from their gender at birth.

Trump’s proposed ban hasn’t fared well in early opinion polls. A Reuters-Ipsos poll Friday found 58 percent of Americans say transgender people should be allowed to serve in the military with 27percent opposed.

A Rasmussen Report poll taken Thursday and Friday asked respondents only whether they agreed with Trump’s statement — “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” — and found that 45 percent disagreed and 44 percent agreed.

The Reuters-Ipsos poll was conducted online among 1,249 adults, and the Rasmussen Reports poll online and by phone among 1,000 likely voters. Both had margins of error of plus or minus 3 percentage points.

Bob Egelko is a San Francisco Chronicle staff writer. Email: BEgelko@sfchronicle.com

Twitter: @egelko