The monarch said he and the Queen were “deeply shocked and saddened” by Monday’s incident in the city.
The head of state, who is currently on a two-day visit in Canada with his wife, said: “It is truly devastating to see that what should have been a joyous celebration for so many could end in such distressing circumstances.
“At this heartbreaking time for the people of Liverpool, I know that the strength of community spirit for which your city is renowned will be a comfort and support to those in need.”
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The Prince and Princess of Wales have also issued a statement, saying they were “deeply saddened” by what happened in Liverpool.
William, who is patron of the Football Association, and his wife Kate said in a message shared by Kensington Palace on social media: “What should have been a joyful celebration ended with tragedy.
“Our thoughts are with those who were injured and to the first responders and emergency services on the ground.”
Meanwhile, the Princess Royal visited the Royal Liverpool University Hospital on Tuesday, where she met medical staff who treated some of the 47 people injured when a vehicle hit fans attending the parade.
Divisional medical director for surgery at Aintree University Hospital, Marc Lucky, told Princess Anne that medics were “very, very fortunate” that there were not more major injuries.
Consultant Jay Rathore added: “Most of the injuries were limb injuries. No life-threatening, we were able to manage them.”
The princess was already due to be in Liverpool on Tuesday to visit the MS Queen Anne after it arrived on Monday for Cunard’s 185th anniversary celebrations.
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She expanded her itinerary to also meet nurses, consultants, and paramedics, as well as representatives from Merseyside Fire and Rescue Service and the football club, in light of Monday night’s incident.
“We really appreciate you still coming, because it will mean a lot to the people of the city,” Liverpool City Council leader Liam Robinson said as he thanked the princess for her visit.
A Buckingham Palace spokesman said: “The princess would like to share her heartfelt condolences and support for the families and communities affected.
“Her Royal Highness also wishes to acknowledge the courage of the emergency services, some of whom she met today, and all those providing care and comfort during this difficult time.”
