Prime Minister Lars Løkke Rasmussen and wife Solrún visited the palace on Sunday to place their own floral tribute to the late Prince Henrik, husband of Queen Margrethe, who died last week aged 83.
"Like everyone else, I wanted to come here and show my personal respect for Prince Henrik and thereby my support for the royal family as a whole," Rasmussen said.
Danes and other well-wishers have turned out in vast numbers since last Tuesday's announcement to leave their floral tributes and messages at the palace.
"It is completely overwhelming. It is wonderful to see the way Danes are showing their respect for Prince Henrik and their affection for the royal family," Rasmussen said.
The PM said the tributes gave a "strong signal" of support to the Queen at a difficult time.
Rasmussen also spoke of how he would remember the late prince.
"I think back to memories of Prince Henrik with great pleasure. He was first and foremost a happy person, and did not just want to be a spectator in life," he said.
"There was always a good atmosphere around him. Good food, good wine, good anecdotes and big arm gestures. He was someone who could put you in a good mood just by their presence," Rasmussen said.
Prince Henrik will be buried on Tuesday at 11am in a ceremony for close family at Christiansborg Slotskirke in Copenhagen.
Prime Minister Rasmussen will also attend the service.
The prince will be cremated, in accordance with his wishes, with half of his ashes to be spread at sea in Danish waters, and half placed in the Fredensborg Palace gardens.