After adulatory crowds in Ottawa, the Duke and Duchess of Cambridge's tour of Canada enters tricky phase in Quebec

The Duke and Duchess of Cambridge faced the first organised protests against their visit to Canada within minutes of their arrival in Montreal on Saturday night.

Demonstrators held up placards denouncing the couple as "parasites" as they arrived at the world renowned Sainte-Justine university hospital. They were heavily outnumbered by others who had come out to cheer the royal couple, but one of the protest organisers, Guillaume Martin, told reporters: "We think the monarchy is something from the middle ages and we don't want to pay for the trip."

The Canadian government, which is meeting the bill, says that the extra cost, equivalent to £950,000, amounts to only a few cents a head for the country's population. The couple ignored the demonstration and spent more than an hour chatting to child cancer patients inside the hospital.

Sunday promises to be more fraught when the royal party moves on to Quebec City, where more protests are planned.

Royal visitors have had an uncertain welcome in Quebec province – where more than 80% of the population speak French – in recent decades. The Queen has not returned to Quebec City since protesters turned their backs on her and booed in 1964, and two years ago Prince Charles and Camilla were held up by scuffles between demonstrators and police as they visited Montreal.

Radical young protesters from the Quebec Resistance Network have called for a demonstration outside the city hall, though they have promised it will be peaceful.

Patrick Bourgeois, leader of the network, said the separatists want to send a message "that the monarchy is not welcome in Quebec".

Prince William has emphasised Canada's bilingualism and dual identity – "Bonne fête, Canada, happy birthday," he exclaimed in a speech.

The visit to Quebec province is a sign that the authorities believe their appearance there will be a success. In a recent poll, more than half of those questioned described themselves as excited by the prospect of seeing them.

During the first two days of their tour in Ottawa, the royal couple have been greeted by huge and adulatory crowds. More than 300,000 people were estimated to have crowded around the capital's Parliament Hill during the Canada Day celebrations on Friday, many of them travelling for hours and some sleeping out to catch a glimpse of the prince and his bride.

Although the duchess has not visited Canada before, her husband has stressed her links to the country, recalling that her grandfather had trained as a pilot in Alberta during the second world war. The Queen has visited Canada more frequently than any other country: 22 times, most recently last year.

The royal couple on Saturday went through the near-obligatory tree-planting ceremony at the governor-general's residence – a Canadian hemlock. They later met military veterans and members of the war brides association at the Canadian war museum – nearly 45,000 young British and European women emigrated to the country after the second world war.

• This article was amended on 8 August 2011 to remove a reference to Quebec City being the heart of the long-established separatist movement.