Gen. Votel and other signatories say they signed the endorsement letter before reports of Gen. Tata’s old tweets emerged, prompting them to reconsider their support.

In a series of remarks on Twitter, Gen. Tata called Islam “the most oppressive, violent religion” and referred to Mr. Obama as a “terrorist leader.” In a radio appearance, he falsely referred to Mr. Obama’s “Islamic roots,” according to CNN, which first reported his remarks June 12.

On May 20, 2018, Gen. Tata, in a twitter argument with former Central Intelligence Agency Director John Brennan, said Mr. Brennan should “pick your poison,” which he said could include sexual humiliation in prison or suicide by gunshot, a tweet that appeared to cross Twitter’s decency rules and was removed.

Retired Air Force Lt. Gen. David Deptula said he was notifying Gen. Tata that he wanted his name removed from the letter.