The touting of her enthusiasm for another run underscores the extent to which Mrs. Romney has been a constant force in not only supporting, but in some ways, propelling her husband’s political career forward.

“Ann believes that if someone can make a difference they should, and she believes very, very strongly that Mitt is capable of making a difference. I’ve heard her express that fundamental concept again and again,” said Grant Bennett, a friend of the couple who succeeded Mr. Romney as bishop in the Mormon Church in Belmont, Mass.

Mrs. Romney declined to comment for this article, but some of her husband’s advisers said he needed to explicitly state his wife’s support after her rather emphatic expressions that, after his defeat in 2012, she was not signing up for another campaign…

But her health has improved, and through hard work and horseback riding, she has remained active, giving inspirational talks, including one in Palm Beach, Fla., this month, about overcoming the challenge of neurological disease. Like her husband, she has also gained strength from a faith that provides them with a sense of personal and political purpose.