BRUSSELS — Belgium's former king this week acknowledged he had fathered a daughter out of wedlock, after getting the results of a court-ordered DNA test.

“His Majesty King Albert II took note of the results of the DNA sample,” lawyer Alain Berenboom said in a statement. “Scientific conclusions indicate that he is the biological father of Ms. Delphine Boël.”

That would also make her the half sister of Belgian’s current monarch, King Philippe.

Boël, a 51-year-old artist, has long sought recognition as Albert’s fourth child.

Her mother, Baroness Sybille de Selys Longchamps, described an 18-year relationship with Albert — a claim that first surfaced in a 1999 biography about Albert’s wife, then-Queen Paola. Boël first talked about it publicly in 2005, and many Belgians had decided she was telling the truth.

Albert, 85, had evaded questions about the affair. But when he abdicated in 2013, citing health reasons, he lost his immunity from prosecution, and Boël pursued her case in the courts.

The former monarch submitted to the DNA test after he was ordered to do so last year by a Belgian judge, with the threat of a 5,000-euro fine for each day he did not comply. He acknowledged the results in the statement released through his attorney Monday.

The statement sought to emphasize a distinction between “legal paternity” and “biological paternity” and asserted that Albert “was not involved in any family, social or educational decision whatsoever relating to Mrs. Delphine Boël.”

The attorney added that Albert wished to “put an end to this painful procedure in honor and dignity.” He did not say for whom the procedure had been painful.

Boël’s attorney, Marc Uyttendaele, told The Washington Post that the relationship between his client and the former king “is in bad shape, sadly.”

“The press release of the king yesterday lacked humanity or even kindness — it is almost surreal,” Uyttendaele said. “He sees himself as a victim . . . but the real one is my client.”

The attorney added: “It is proven now: He is the biological father. But he never took responsibility.”

Belgian news outlets noted that as a descendant of the king, Boël presumably would be entitled to a portion of his estate. But under the Belgian constitution, only legitimate descendants of the king and queen enter the line of royal succession.

Philippe’s full relations already stretch far back in that line, as he has four children. His eldest daughter, Princess Elisabeth, the Duchess of Brabant, 18, is his heir apparent.

Albert, the second son of King Leopold III, did not grow up expecting to become monarch. But his elder brother, King Baudouin, died of heart failure in 1993. And because Baudouin had no children, Albert inherited the throne.

Boël has said that Albert played a quiet role in her early life but that he distanced himself after the claims about his affair with her mother became public.

Albert’s wife, Paola, an Italian aristocrat, is popular among Belgians. She and her husband came close to divorce before making up. The two are now spotted together at the sorts of events attended by former monarchs: Belgian national days, parades, christenings.

Belgium is a constitutional monarchy in which the king has little formal power. But in a society that is riven between ethnic and linguistic groups — the country is split between the French-speaking Walloons and the Dutch-speaking Flemish, and few people describe themselves as Belgian — the king is one of the few truly Belgian symbols.

The king also plays a role in breaking political deadlocks following elections, since he decides who can have the chance to form a coalition government, a significant power given the country’s fractured political landscape. Albert was critical in bringing to a close the country’s record-setting 541 days of coalition negotiations in 2011, and Philippe is now enmeshed in negotiations that have stretched since May elections.

Boël has incorporated royal themes into her artistic work. In one sculpture, a black-spotted cow appears to be wearing a green-and-gold crown. Her friends told Belgian news outlets that she decided in 2013 to publicize her effort to be recognized as Albert’s daughter after one of her own daughters was hospitalized with pneumonia and she felt more keenly the absence of a father.

Quentin Ariès contributed to this report.