(CNN) The Log Cabin Republicans, one of the country's most influential LGBT Republican groups, announced Saturday that it would not back the party's presidential nominee, Donald Trump.
The group, while praising Trump as "perhaps the most pro-LGBT presidential nominee in the history of the Republican Party," said it had objections to views held by some of Trump's advisers and his support for a bill that would protect people who disagree with same-sex marriage from federal penalties.
"Log Cabin Republicans have long emphasized that we are not a single-issue organization, nor are our members single-issue voters," the group said in a press release. It added that it will instead focus on down-ballot races to preserve Republican majorities in Congress.
Trump has occasionally mentioned LGBT Americans as a presidential candidate, most notably in the aftermath of the attack on a gay Orlando nightclub in June and his acceptance speech at the Republican convention in July. In that speech, The Washington Blade noted, he became the first GOP nominee to positively mention LGBT rights in that setting.
"As Mr. Trump spoke positively about the LGBT community in the United States, he concurrently surrounded himself with senior advisers with a record of opposing LGBT equality, and committed himself to supporting legislation such as the so-called 'First Amendment Defense Act' that Log Cabin Republicans opposes," Log Cabin Republicans said.
A message left with Trump's campaign seeking response was not immediately returned.
Trump's running mate, Indiana Gov. Mike Pence, has been criticized for his support of a law that would have allowed businesses to turn away gay and lesbian customers in the name of religious freedom.
The group criticized the Republican Party in July for not backing a pro-LGBT platform.
"There's no way to sugar-coat this: I'm mad as hell -- and I know you are, too," Gregory Angelo, president of the Log Cabin Republicans, said in a fundraising email at the time. "Moments ago, the Republican Party passed the most anti-LGBT Platform in the party's 162-year history."
The platform expressed opposition to same-sex marriage, a lack of support for allowing transgender people to use the restrooms of their choice and support for conversion therapy, Angelo said.
The group, however, left open the possibility Saturday that it could eventually support Trump.
"Should Mr. Trump become our nation's next President, Log Cabin Republicans welcomes the opportunity to work with his administration to ensure the advances in LGBT freedom we have fought for and secured will continue," the press release said. "Until and unless that happens, our trust would be misplaced."