On Tuesday, the royal family, prime minister and France's ambassador to Denmark were among those who attended a private service at the Christiansborg Palace Chapel in the centre of Copenhagen, while a few hundred people gathered outside to pay their respects.

"I've come to say goodbye to the prince. It means a lot to me as an immigrant that even though he was born outside Denmark he still became a part of the royal family," said Iraqi-born Makarim Ibrahim, 51.

Some 20,000 Danes have visited Prince Henrik's coffin in the past three days while he lay in state.

Last August Henrik said that he did not wish to be buried next to the queen, breaking a 459-year-old tradition.

Shortly afterwards, the palace issued a statement saying that he had dementia.

The 83-year-old French-born prince died in his sleep last week.

It was afterwards announced that the palace would respect his wish not to be buried in a tomb in Roskilde Cathedral prepared for him and Margrethe, who he said had never acknowledged him as her equal.

Instead, Henrik's body will be cremated and half of the ashes scattered in Danish waters and half buried in the garden of Fredensborg Castle, north of Copenhagen, where he died.

As in most monarchies, a Danish princess becomes queen when her husband takes the throne, but a man does not become king through being married to a queen.

Henrik is survived by his wife, sons Crown Prince Frederik, Princess Mary's husband, and Prince Joachim, and eight grandchildren.

Australian Associated Press