“It was probably the most surprising letter I have received in my professional career,” Mr. Stephenson said in an interview on Thursday afternoon. “If one of my executives had sent Kathy a letter that unprofessional, I would want to know.”

After he sent the email, Ms. Hopinkah Hannan apologized to him in a letter on Wednesday, a copy of which was provided to The New York Times by someone close to the Boy Scouts. “I apologize that my comments may have suggested something other than my highest regard for you personally, the Boy Scouts of America and the path forward for our organizations,” she wrote.

Ms. Hopinkah Hannan did not return an email and a phone call seeking comment on Thursday.

“We stand fully behind our girls, our councils and our national leadership in working to ensure that the needs of girls remain at the forefront of any dialogue,” Mike Lopes, a spokesman for the Girl Scouts, said in a statement.

The Boy Scouts and the Girl Scouts each have millions of participants. But they have been buffeted by societal changes affecting youth organizations, leading to membership declines and forcing them to find new ways to attract members. The Boy Scouts have also had their own challenges and only recently started accepting gay scout leaders and transgender scouts after heavy criticism.

Effie Delimarkos, a spokeswoman for the Boy Scouts, said families had increasingly asked the Boy Scouts for options for girls. The phone call last week was set up to discuss ways the two groups could work together toward that goal, she said.

“How do we essentially listen to the families that have been bringing their daughters along with their sons to pack meetings?” Ms. Delimarkos said in an interview Wednesday night.