May was welcomed on her first official visit to Canada's parliament by a military guard before sitting down with Prime Minister Justin Trudeau.
"There is an awful lot for us to talk about in our bilateral relationship and how we can build on the relationship with CETA," May said.
The EU-Canada Comprehensive Economic and Trade Agreement (CETA) is to provisionally take effect on Thursday, removing 99 per cent of customs duties between the two sides.
A spokesman for Downing Street said earlier that Britain hopes to "use (CETA) as the basis of our own bilateral trading arrangement (with Canada) once we have left the EU."
Trudeau said he looked forward to discussing "opportunities to continue working closely with the United Kingdom as it moves forward with Brexit."
"We'll make sure that the relationship between Canada and the UK stays as strong as it always has been and continues to with that seamless transition," he said.
His comments drew praise from eurosceptic members of his Conservative party, while others saw it as an attempt to force May's hand ahead of a Friday speech in the Italian city of Florence, when she will give an update on her plans and the progress of negotiations with the EU.
After her meeting with Trudeau, May will travel to New York tomorrow for the UN General Assembly.
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