A low-key, non-state service was held inside the chapel, attended by 60 close family members and senior representatives from Denmark's government, including Prime Minister Lars Løkke Rasmussen.
Royal chaplain Erik Norman Svendsen gave the funeral service, after which hymns were sung by choirs inside the chapel.
Ten red-clad Royal Life Guards, all veterans of service abroad, carried the casket to the hearse in front of subdued members of the public at Christiansborg.
Photo: Mads Claus Rasmussen/Scanpix Denmark
A guard of honour, composed of various military companies, stood outside the palace as the music corps band began to play 'Prince Henrik's March of Honour'.
Queen Margrethe, who was wearing a black veil, looked on from the entrance to the church, accompanied by her children and grandchildren.
Meanwhile, an honorary salute was fired from Christian the Sixth's Battery at the nearby Holmen naval base.
An emotional royal family could, via live broadcasts, be seen holding each other's hands during the service.
Royal Chaplain Svendsen gave an honest and unsentimental speech as part of his sermon, as he touched upon the prince's larger-than-life personality, sometimes-difficult relationship with the media and his role within the royal family.
"The prince was very much his own man and laid his hat where he pleased. Colourful, fearless and French. That often resonated with the press… there was a period in which the prince felt directly bullied," Svendsen said.
Eva Uvan Handberg was one of the many members of the public who came to watch the occasion from outside Christiansborg.
"[I wanted to] honour him for the passion he had, and what he did. The Danish media was never really good at showing these things, all the diverse and dedicated things he did. I've been thinking this last week that Jante's law never really got to Prince Henrik. There's a dignity here today and I'm very moved by that," Handberg told The Local.
Norwegian Handberg, who lives in Copenhagen, also praised the late prince as a role model for other foreigners living in Denmark.
"I come from Norway, so I know what it's like never to become thoroughly Danish. [There was a] double standard of [media and public] not respecting him really or not taking him seriously, and I think the struggle of feeling at home in a foreign country is an important thing, and I admire this guy for always being true to himself," she said.
In accordance with his wishes, the prince is to be cremated, with some of his ashes spread at sea in Danish waters and the remainder to be kept in the gardens at royal summer residence Fredensborg Palace north of Copenhagen, where he died last Tuesday aged 83.
A sea of flowers has been left by well-wishers in front of royal residence Amalienborg Palace over the last week, while over 19,000 people visited the prince's closed casket at Christiansborg Palace Chapel between Saturday and Monday.
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