“American Mirror,” by Deborah Solomon, a 493-page account of the life and work of Rockwell, an illustrator for The Saturday Evening Post for nearly 50 years, was published last month by Farrar, Straus and Giroux.

In the book, Ms. Solomon raises the question of whether Rockwell was gay, writing that he “demonstrated an intense need for emotional and physical closeness with men,” and that his marriages may have been a strategy for “controlling his homoerotic desires.” She described a camping trip in Quebec that Rockwell took with his male assistant, during which the men swam and played cards together late into the night, and Rockwell noted in his diaries that his assistant looked “most fetching in his long flannels.” There is nothing, Ms. Solomon cautioned in the book, “to suggest that he had sex with men.”

Later in the book, Ms. Solomon writes that “we are made to wonder whether Rockwell’s complicated interest in the depiction of preadolescent boys was shadowed by pedophilic impulses.” She again added a disclaimer: “There is no evidence that he acted on his impulses or behaved in a way that was inappropriate for its time.”

But the mere insinuations have infuriated members of the Rockwell family intent on protecting his legacy. Two family members, who spoke in an interview on Monday, said that they regarded Ms. Solomon’s book as “shocking.”

“The bottom line is that’s it’s astonishing,” said Abigail Rockwell, a granddaughter of the painter, who said he was heterosexual and “not remotely a repressed man.”

“She layers the whole biography with these innuendos,” Ms. Rockwell added. “These things she’s writing about Norman Rockwell are simply not true.”

Thomas Rockwell, the second of Rockwell’s three sons, said the family fully cooperated with the biography. “We were perfectly open” with Ms. Solomon, he said, “because we liked her.”

The family plans to release a statement on Tuesday saying that Ms. Solomon’s purpose in writing the book was “publicity and financial gain and self-aggrandizement.”

The Rockwell family’s statements have drawn a sudden spotlight to portions of the book that, until now, had not been the center of discussions of the book in the press.

Reviewing the book in The New York Times, John Wilmerding made brief mention of the question of whether Rockwell was a “repressed homosexual,” but spent most of the review discussing Ms. Solomon’s broader account of his life and artistic accomplishments. The book, he wrote, “takes shape through compact vignettes of people and events, appropriate to Rockwell’s self-contained aphoristic depictions and often silhouetted figure groupings.”

Ms. Solomon, when told of the Rockwell family’s statements, said that the discussion of Rockwell’s sexuality was “a tiny part” of the book.

“The discussion is really about his work,” she said. “I feel like this is really the first book that convincingly makes the case for Rockwell’s artistic importance, and I would hope to keep the discussion on that subject.”

Asked whether she believes Rockwell was gay, she said, “I’m a biographer, I am not a psychiatrist. I would never presume to say that someone is gay. But I do feel entitled as an art critic and an art historian to analyze works of art. And I do think a case can be made that some of Rockwell’s paintings display homoerotic tendencies. He specialized in affectionate portrayals of the male figure and lamented many times that he could never paint a sexy woman. And nowhere in the book do I say that he is gay.”

Ms. Solomon said that she had not heard directly from any members of the family about the book.

Farrar, Straus and Giroux, which published the book on Nov. 5, said in a statement, “We have complete confidence in Deborah Solomon as a biographer and art historian and in the importance of her new book on Norman Rockwell, which argues strongly and in fresh ways for his achievements as an American master.”

Jeff Seroy, a spokesman for Farrar, Straus, said that 15,942 copies are in print. More than 2,600 copies have been sold in hardcover and almost 500 copies in e-book format.

On Wednesday, an auction of three of Rockwell’s most popular paintings will take place at Sotheby’s, works that could bring more than $30 million.

Asked why the family members waited weeks after publication to raise objections to the book, Ms. Rockwell said that they have debated whether to speak out but were spurred forward when the book received positive media attention, and Ms. Solomon began to be treated as “a Norman Rockwell authority.” Ms. Solomon, the author of biographies of Jackson Pollock and Joseph Cornell, is also a frequent contributor to The Times and a former columnist for The New York Times Magazine.

“We’ve asked ourselves over and over again, should we come forward or let this thing die?” Ms. Rockwell said. “People are now starting to refer to Pop,” she added, using her grandfather’s nickname, “as a closeted homosexual. This is dangerously becoming fact.”