Marc Uyttendaele, Ms. Boël’s lawyer, said on Tuesday that she was “relieved” to be “considered as a legitimate child” because it would “put an end to the social exclusion that she was subjected to and will prevent her children from having to bear this burden.”

But Mr. Uyttendaele added that she had been “hurt” by the “coldness” of the king’s statement.

In it, the king’s lawyers said that he had “never been involved with any family, social or educative decision whatsoever regarding Madame Delphine Boël” and that it was Ms. Boël who, “40 years later,” had decided to “change families” through a “long” and “painful” lawsuit.

“The attitude taken by Albert II yesterday does not foretell the opening of a dialogue between his daughter and him,” Mr. Uyttendaele said. “For her part, she is open to this dialogue, but without much hope.”

King Albert II was a second son and, as such, was not expected to succeed to the throne. Instead, he enjoyed a lavish lifestyle of parties and travel, and when Ms. Boël was born in 1968, the prince privately recognized her as his daughter and cared for her, according to her lawyer.

But Albert’s elder brother, King Baudouin, died suddenly of heart failure in 1993, leaving no children, meaning Albert became king. According to Ms. Boël, that is when her biological father, seeking to avoid a scandal, cut all ties.

Ms. Boël will not enter the royal line of succession, but she will be in line to inherit some part of the king’s private fortune. Her lawyer, however, stressed that she had filed the suit for emotional reasons, not financial ones, noting that Jacques Boël, who raised Ms. Boël as his only daughter, was a wealthy man.

“Her motives were therefore in no way profit-seeking — quite the opposite,” Mr. Uyttendaele said.