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Orrin Hatch.
Top Republicans such as Sens. Orrin Hatch, John McCain, Joni Ernst, Richard Shelby, and Lindsey Graham all expressed disapproval with the president's Wednesday morning tweets.
"I don't think we should be discriminating against anyone," Hatch, a Utah Republican, said in a statement. "Transgender people are people, and deserve the best we can do for them. I look forward to getting much more information and clarity from our military leaders about the policy the president tweeted today."
McCain, the Arizona Republican who chairs the Senate Armed Services Committee, said Trump's early-morning tweets were "yet another example of why major policy announcements should not be made via Twitter" and called them "unclear."
"The Department of Defense has already decided to allow currently serving transgender individuals to stay in the military, and many are serving honorably today," he said in a statement. "Any American who meets current medical and readiness standards should be allowed to continue serving. There is no reason to force service members who are able to fight, train, and deploy to leave the military - regardless of their gender identity."
McCain also noted that the Defense Department "is currently conducting a study on the medical obligations it would incur, the impact on military readiness, and related questions associated with the accession of transgender individuals who are not currently serving in uniform and wish to join the military."
McCain said no new policy regarding transgender servicemembers "is appropriate" until the Defense Department study is completed, reviewed by Defense Secretary Jim Mattis, military leaders, and members of Congress.
First told of the tweets during a CNN interview, Shelby, an Alabama Republican, expressed a willingness to allow transgender people serve in the military.
"You ought to treat everybody fairly and you ought to give everybody a chance to serve," he said.
A spokeswoman for Ernst, an Iowa Republican and a veteran, told Politico that the senator has served with people "from all different backgrounds" and that gender identity is not an indicator of a person's military capability.
"She believes what is most important is making sure servicemembers can meet the physical training standards, and the willingness to defend our freedoms and way of life," the spokeswoman said. "Americans who are qualified and can meet the standards to serve in the military should be afforded that opportunity."
And Graham, the South Carolina Republican, said "we shouldn't make our decisions based on a tweet."
Trump began Wednesday by announcing that the military would no longer allow transgender Americans to serve, claiming that he consulted with "my generals and military experts" who cited "tremendous medical costs and disruption."
"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 pair of tweets.
The announcement is a reversal of President Barack Obama's 2016 move which allowed transgender people to openly serve in the military, although Mattis had delayed the policy's implementation.
A 2016 RAND Corporation study found that up to 10,700 transgender people may already serve. That study estimated that 29 to 129 of the military's 1.4 million troops incurred medical costs related to their transgender status. In total, the study found that the military spent roughly $8 million on such medical services. The military spends more than $41 million on the erectile dysfunction drug Viagra.
Some Republicans did come out in favor of Trump's Wednesday proclamation.
Rep. Vicky Hartzler, a Missouri Republican, tweeted she was "pleased to hear that [Trump] shares my readiness and cost concerns, & will be changing this costly and damaging policy."