The spat highlighted the continuing challenge to reviving a pact whose survival was thrown into doubt when President Donald Trump ditched it, in one of his first acts in office, in favour of bilateral dealmaking.
Japan had lobbied hard to proceed with a pact that could also help to contain China's growing regional dominance, ahead of talks in the Vietnamese resort of Danang this week alongside Asia Pacific Economic Cooperation (APEC) meetings.
Some other members have not shown a readiness to move so fast.
Asked by reporters about the results of a meeting of TPP ministers, Japanese Economy Minister Toshimitsu Motegi said "(they) agree in principle", adding that the ministers had finalised "a list of suspensions" - clauses that would be suspended to avoid renegotiating the whole agreement.
But Candian Trade Minister Francois-Philippe Champagne later said on Twitter: "Despite reports, there is no agreement in principle on TPP."
The TPP aims to eliminate tariffs on industrial and farm products across a bloc whose trade totalled $356 billion last year. It also has provisions for protecting everything from labour rights to the environment to intellectual property - one of the main sticking points.
Canada, whose economy is the second biggest among the TPP-11 after Japan, said on Wednesday it would not be rushed into a revived TPP deal. Like Mexico, its position is further complicated by renegotiation of the North American Free Trade Agreement (NAFTA) with the Trump administration.
Mexico's trade minister said on Thursday the TPP countries had reached agreement in talks, but he gave no details and said there would be an announcement on Friday.
The leaders of TPP countries are tentatively scheduled to meet on Friday to discuss the proposals of ministers.
One Canadian official who declined to be named said ministers from different countries may have had different interpretations of Thursday's discussions.
Options discussed by the TPP countries have included suspending some provisions of the original agreement to avoid having to renegotiate it and potentially to entice the United States back in the long term.
Trump and other APEC leaders, including President Xi Jinping of China and Russian President Vladimir Putin, will meet on Friday in Danang.
APEC trade and foreign ministers separately ended a meeting on Thursday with a "very good outcome", despite differing views on trade and protectionism, Vietnamese Trade Minister Tran Tuan Anh said.
Ministerial talks on a communique for the APEC leaders were extended into a second day on Thursday in the face of U.S. demands for changes to the language used concerning issues such as free trade and protectionism, officials at the talks said.
(Additional reporting by A. Ananthalakshmi; editing by Andrew Roche)
By Mai Nguyen