Trudeau made the remarks Wednesday when asked whether he would walk away from the 11-country trade pact if the revised deal failed to include several new "progressive" chapters Canada has been pushing for.
"We believe that progressive, solid trade deals can help citizens in all sorts of different countries, at different levels of development and our ministers are very much focused on that," Trudeau told reporters in Hanoi, where he started his multi-day trip through Southeast Asia.
"But let me, of course, remind everyone that Canada will not be rushed into a deal that is not in the best interests of Canada and of Canadians."
Trudeau then added, in French: "I can assure people that we will not be rushed into signing a deal at all costs."
Canada will not be rushed into a deal that is not in the best interests of Canada and of Canadians.Prime Minister Justin Trudeau
The remaining TPP economies are trying to revive the deal following President Donald Trump's decision to withdraw earlier this year.
The TPP is expected to be a central theme at this week's Asia-Pacific Economic Co-operation summit in the Vietnamese city of Danang. Trudeau will attend the APEC meetings and there has been speculation that some kind of deal could be reached by the end of the summit.
International Trade Minister Francois-Philippe Champagne has said Canada wants the updated TPP to contain progressive chapters on the environment as well as workers' and women's rights.
But trade experts have predicted that persuading Asia-Pacific economies on progressive chapters will be a tough sell.
Some of the countries at the table are far less developed than Canada and would have difficulty implementing them, while others might prefer to leave social issues separate from trade agreements.
Trudeau is travelling in the Asia-Pacific over the next week to strengthen Canada's ties to the region.
He arrived Wednesday in the buzzing, moped-filled city of Hanoi. It's the capital of a fast-growing country that has a deep cultural connection for many Canadians.
Trudeau met Vietnamese President Tran Dai Quang, Prime Minister Nguyen Xuan Phuc and civil society leaders, with whom he discussed issues like human rights, gender equality and freedom of expression.
On Thursday, he's scheduled to travel to Ho Chi Minh City to visit the stock exchange, hold a roundtable with business leaders and appear at a university event.
He will head to Danang on Saturday for the two-day APEC leaders' summit, before moving on to the Philippines to attend the annual meetings of the Association of Southeast Asian Nations.
At both the APEC and ASEAN events, Canada is expected to press its trade agenda. It's already engaged in exploratory trade talks with the ASEAN countries as well as negotiations to salvage the TPP.
Vietnam could be key partner: expert
When it comes to the members of the TPP, much of the focus remains on Japan, the world's third-largest economy.
But Vietnam is also at the TPP table and it's an ASEAN member, which sets it up as a key partner in a region where Canada wants to increase its presence.
Vietnam, projected to see economic growth this year of 6.3 per cent, features a sturdy consumer base, an emerging business class and an expanding footprint in supply chains.
Dominic Barton, the global managing partner of consulting giant McKinsey & Co., said in an interview that the rapid changes in Vietnam's key cities remind him, in some respects, of what Shanghai went through less than two decades ago.
Barton, who also chairs the Trudeau government's economic growth council, said Vietnam is an example of why Canada must be "motoring ahead" into Asia, particularly with so much uncertainty around the renegotiation of the North American Free Trade Agreement.
"We've got to go hard on those Asian relationships," said Barton, who led McKinsey operations in Asia and South Korea for nearly a decade.
"I think we just have to have irons in many fires."
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Dan Ciuriak, a former deputy chief economist for what is now known as Global Affairs Canada, believes an updated TPP pact is closer to fruition than Canada's potential deals with ASEAN or China.
"Vietnam and Japan would be the two biggies for Canada in terms of diversifying trade," said Ciuriak, who is now the director of Ciuriak Consulting Inc.
There are other parts of the original TPP where Canada would like to see modifications.
A senior government official has said Canadian negotiators are seeking changes to the original TPP in several areas, such as its intellectual-property provisions, cultural exemptions and its impact on Canada's supply management system for dairy, poultry and eggs.
Former Quebec premier Jean Charest, who is honorary chair of the ASEAN-Canada Business Council, said Vietnam not only shows real economic potential, it also has strong people-to-people links with Canada.
Both countries have French heritages and both are members of la Francophonie, he said in an interview.
'Boat people' forged unique bond
But Charest said it's the story of the Vietnamese refugees, or boat people, who came to Canada in the late 1970s that really forged the bond.
By 1980, around 60,000 people from Vietnam, Cambodia and Laos arrived in Canada after fleeing violence in their homelands. Today, about 240,000 people in Canada have Vietnamese roots.
"Certainly, the story of the boat people in Quebec, I can tell you without hesitation that it resonates positively in the minds of Quebecers as being a good example of integration into the broader Quebec society," said Charest.
However, when looking at today's Vietnam, Charest said the promising economy is accompanied by negatives, such as the fact "it is a communist regime and everything that comes with it."
Canada's pursuit of a more open trading relationship with Vietnam comes with pressure to have frank discussions about the serious concerns over the communist government's human-rights record.
PM pushed to speak out on human rights
Human Rights Watch calls the Vietnam's record "dire in all areas" because of the Communist party's firm grip on political power. The group also said the government has harassed, intimidated, physically harmed and jailed its opponents.
Earlier this week, Conservative Sen. Thanh Hai Ngo urged Trudeau to use his time with Vietnamese leaders to raise Canada's "serious concerns" about Vietnam's human-rights abuses, such as its suppression of a growing democratic movement.
Canada and Vietnam signed a partnership agreement Wednesday that would focus on deepening co-operation in many areas, like trade, security and cultural exchanges.
Trudeau told reporters the agreement would also help advance the countries' ongoing dialogue on human rights.