(CNN) Discussions are ongoing in Canada over who will pay the costs of the Duke and Duchess of Sussex's security for their proposed new life in the country, according to Prime Minister Justin Trudeau.

Queen Elizabeth II on Monday agreed to a "period of transition" while details of a more "independent" role for Harry and Meghan are hammered out. They will spend time in both the UK and Canada during this period.

The couple announced last week that they wish to step down as senior British royals and live part-time in North America.

Trudeau told a Canadian television station Monday that: "...there are still a lot of decisions to be taken by the royal family, by the Sussexes themselves, as to what level of engagement they choose to have and these are things that we are obviously supportive of their reflections, but have responsibilities in that as well."

Trudeau added: "That is part of the reflection that needs to be had and there are discussions going on."