Story highlights The group criticized the Republican Party in July for not backing a pro-LGBT platform

The group will now focus on down-ballot races

Washington (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.

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