The EU-Canadian deal, which has been seven years in the making, was due to be finalised at the European Union summit but risks collapsing following opposition from a Belgian regional government.
May has not yet outlined her strategy for implementing the June vote to leave the EU, but has left open the possibility that Britain might leave the bloc's single market and replace it with a new trade arrangement.
After her first EU summit concluded today, she said she supported the Canadian deal but added: "We're not looking to replicate a model that somebody else has."
The Conservative leader is expected to start the formal two-year exit process by the end of March, putting Britain on course to leave the EU by early 2019.
The near-collapse of the EU-Canada deal has however prompted fears for an eventual British deal.
"If the EU does not succeed in agreeing a commercial or economic treaty with Canada, it will be difficult to do so with Britain," Belgian Prime Minister Charles Michel warned.
May has said she wants to control immigration and remove Britain from the jurisdiction of the European Court of Justice -- both requirements of single market membership.
At her first bilateral meeting with European Commission chief Jean-Claude Juncker today, May repeated her desire for immigration controls and a "positive outcome" for trade in goods and services, her spokeswoman said.
Britain cannot begin trade talks with non-EU countries until it has left, prompting concern among businesses that it could leave the single market with no new deals in place.
"This will not undermine the EU's trade agenda, it is not even in competition with it. We will continue to help the EU reach those important trade agreements.
"It's about seizing the opportunities of Brexit and forging an ambitious and optimistic new role for Britain in the world.
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