Albert II, who abdicated from the Belgian throne six years ago, has agreed to a DNA test demanded by a woman who claims to be his daughter in what could be a breakthrough in the long-running case, lawyers have said.

Albert, 84, who stood down from the throne in 2013 for health reasons, had been facing a daily fine of €5,000 (£4,415) for failing to provide his DNA in the case brought by Delphine Boël, 51.

Boël has been trying to prove Albert is her biological father for years and her story has often made headlines. Albert has never publicly denied being her father but had refused to provide DNA.

A statement from Albert’s lawyer, delivered to the Belgian media, said the former monarch had taken note of the judgment two weeks ago imposing the daily fine, and would submit to the test “out of respect to the judicial authorities”. It was made clear the move did not imply any admission of guilt.

Boël’s lawyer, Yves-Henri Leleu, said his client “reacted very positively, because with the DNA test, the biological evidence is now there”.

The lawyer for the former monarch said the DNA results would have to be sealed until later in the legal case.

Rumours about a relationship between Albert and Boël’s mother, Baroness Sybille de Selys Longchamps, the aristocratic wife of an industrialist, have been circulating for years. But the news the king may have had a child with her emerged when a biography of Albert’s wife, Queen Paola, was published in 1999.

In his Christmas message to the nation that year, Albert indirectly confessed to a past infidelity and said he and Queen Paola lived through a “crisis” in the late 1960s that almost ended their marriage but they overcame their marital problems “a long while ago”.

Six years ago, Boël, who has a striking resemblance to some members of the royal family, opened court proceedings to prove Albert was her father.

Boël, an artist and sculptor, has always said she brought the paternity case out of anger at being cold-shouldered by the royal family.