In a statement that was posted on Wednesday evening alongside a WhiteHouse.gov petition begun in honor of Ms. Alcorn, Mr. Obama condemned the practice, sometimes called “conversion” or “reparative” therapy, which is supported by some socially conservative organizations and religious doctors.

The petition has received more than 120,000 signatures in three months.

“We share your concern about its potentially devastating effects on the lives of transgender as well as gay, lesbian, bisexual and queer youth,” the statement, written by Valerie Jarrett, a senior adviser to Mr. Obama, says. “As part of our dedication to protecting America’s youth, this administration supports efforts to ban the use of conversion therapy for minors.”