It follows growing anger on the continent towards pharmaceutical company AstraZeneca, which is accused of failing to deliver the promised number of doses of the COVID-19 vaccine it developed with Oxford University.
On Tuesday, NHS England chief Sir Simon Stevens told MPs that the uproar was due to limited supplies of vaccines.
The EU, which approved the Pfizer-BioNTech and Moderna products later than countries such as Canada, the USA and the United Kingdom, has been criticized for the slow vaccine rollout in many member countries.
AstraZeneca's smaller supply is an especially bitter pill for Europe, since Pfizer said earlier this month that it was also facing delays - proving a disastrous start for Europe's immunization campaign for COVID-19 that started just a month ago.
Sources close to AstraZeneca said dedicated supply chains had been set up for each worldwide agreement to prevent countries squabbling over the same doses.
AstraZeneca last Friday blamed "reduced yields" in its European supply chain for the dose delay.
However, Pfizer also announced recently it was temporarily slowing down production of its vaccine.
German daily newspapers, Handelsblatt and Bild, cited anonymous sources in Germany's government as alleging that the AstraZeneca-Oxford vaccine had an efficacy rate of 8% among the elderly, those 65 years old and above.
On Tuesday, Trudeau responded to concerns that the European Union might limit the supply of vaccines to non-European countries.
Right now, he said Canada is "not involved in those European concerns", noting that AstraZeneca's vaccine is still pending in the country.
The UK has not yet received any of the Moderna jab - the third vaccine approved by regulators - and does not expect to get any until Spring. The shot is expected to be approved for use in Europe later this week.
And around 7 million doses have been administered by health professionals, meaning the country is leading in total doses relative to its population compared to other European Union countries.
Norway, which was not a member of the European Union, was now reportedly expecting to receive less than 18% of the doses that it had signed up for.
While not yet approved by Health Canada, Trudeau said Canada now does not have plans to source its 20 million doses of the AstraZeneca vaccine from European manufacturers.
Prime Minister Boris Johnson said: "I don't want to see restrictions on the supply of PPE across borders, restrictions on the supply of drugs, restrictions on vaccines or their ingredients".
The total projected amount of Pfizer COVID-19 vaccine supplied to Britain between January and March is unchanged by a planned upgrade at a production facility.
Following AZ's announcement Friday, European officials were set to meet with AstraZeneca executives on Monday to seek clarification, Reuters reports; one European official had called AstraZeneca CEO Pascal Soriot ahead of the meeting.
President Joe Biden has already invoked the act to push for faster production of PPE and vaccines.