Unlike Trump so far, Tillerson recognizes Pride Month: 'We will continue to support the human rights of LGBTI persons'

"We will continue to support the human rights of LGBTI persons," he said.

And the omission of June's recognition as Pride Month was particularly curious to many people, considering the president recognized June as Great Outdoors Month, African-American Music Appreciation Month, National Ocean Month and National Homeownership Month.

Tillerson also addressed the discrimination and violence individuals who identify as LGBTI endure.

"We also recognize that LGBTI persons continue to face the threat of violence and discrimination," he wrote. "Violence and discrimination targeting any vulnerable group undermines our collective security as well as American values. When all persons are protected on the basis of equality and with dignity, global stability is strengthened. We will continue to support the human rights of LGBTI persons together with like-minded governments, businesses, and civil society organizations globally."

He continued, "The United States remains committed to human rights and fundamental freedoms for all persons. Dignity and equality for all persons are among our founding constitutional principles, and these principles continue to drive U.S. diplomacy."

A subsequent tweet read, "I am proud to support my LGBTQ friends and the LGBTQ Americans who have made immense contributions to our society and economy."