Turley, chairman and chief executive of Ernst & Young, said in a statement Tuesday that including gays would make the Boy Scouts a "better organization."
"As CEO, I know that having an inclusive culture produces the best results, is the right thing for our people and makes us a better organization," Turley said. "My experience has led me to believe that an inclusive environment is important throughout our society and I am proud to be a leader on this issue.
"I support the meaningful work of the Boy Scouts in preparing young people for adventure, leadership, learning and service; however, the membership policy is not one I would personally endorse. As I have done in leading Ernst & Young to being a most inclusive organization, I intend to continue to work from within the BSA Board to actively encourage dialogue and sustainable progress."
The Boy Scouts of America said in a statement to the Los Angeles Times it "respects the opinions of our board members and [is] thankful for their leadership."
"While we have supporters and board members with different viewpoints on this issue, and who may choose a different direction for their organizations, we believe that good people can personally disagree on this topic and still work together to accomplish the mission of Boy Scouts of America," the statement said.
Jennifer Tyrrell, a former Tiger Cub den leader in Bridgeport, Ohio, has started a petition to be reinstated after she was removed from her post because she is gay. She also started a separate petition asking another board member and gay-rights advocate, AT&T Chairman and Chief Executive Randall Stephenson, to join the cause.
"If Randall Stephenson has been so successful at leading a company committed to LGBT rights, he can use his power as a board member of the Boy Scouts of America to help change a discriminatory policy that prevents families like mine from being involved in Scouts," the petition states.
Stephenson released a statement calling for change from within.
"Diversity and inclusion are part of AT&T's culture and operations, and we're proud to be recognized as a leader in this area. We don't agree with every policy of every organization we support, nor would we expect them to agree with us on everything. Our belief is that change at any organization must come from within to be successful and sustainable," Stephenson's statement said.