"It is the intention of my administration to deal directly with individual countries on a one-on-one (or bilateral) basis in negotiating future trade deals," Trump said in a memorandum to the UN trade representative.
"I hereby direct you to withdraw the United States as a signatory to the TPP, to permanently withdraw the United States from TPP negotiations, and to begin pursuing, wherever possible, bilateral trade negotiations to promote American industry, protect American workers, and raise American wages," the memorandum said.
The TPP is a trade agreement between 12 countries on the border of the Pacific Ocean: Australia, New Zealand, Canada, Singapore, Vietnam, Malaysia, Japan, Mexico, Peru, Brunei, Chile and, until now, the US.
Australia and New Zealand have responded to the US withdrawal by saying that they hope to press ahead with the agreement.
"The TPP is an agreement of unprecedented scope and ambition. [It] is too important as a driver of the creation of more Australian jobs not to do all we can to see the agreement enter into force," the Australian government said.
New Zealand prime minister Bill English told local media that Trump's withdrawal from the TPP was not unexpected, but was disappointing, and that perhaps the remaining 11 nations could go ahead but allow the US to join at a later date after Trump leaves office.
Malaysia's international trade minister Mustapa Mohamed said it will be a "missed opportunity" for the country if the TPP plan fails.
"A number of research houses have singled us out as a clear winner in the TPP," he said.
"Should the TPP fail to materialise, our focus would be to enhance the economic integration of Asean in the context of the Asean Economic Community Blueprint 2025, push for the timely conclusion of the Regional Comprehensive Economic Partnership, as well as pursue bilateral free trade agreements including with TPP members whom we currently do not have any preferential trading arrangement," he said.
Singapore, however, will now look to other trade initiatives rather than trying to revive TPP. A spokesman for the Ministry of Trade and Industry told Singapore's Business Times that "without the participation of the US, the TPP agreement as signed cannot come into effect".
Instead, Singapore is looking at other regional integration initiatives such as the Regional Comprehensive Economic Partnership and the proposal for a free trade area of the Asia-Pacific, the spokesman said.
"Singapore will continue to participate in these initiatives. We will have to discuss the way forward with the other TPP partners. Each of the partners will have to carefully study the new balance of benefits," he told the Business Times.
Japan's government spokesman Koichi Hagiuda said it was "meaningless" to have the TPP without the US and Tokyo is not interested in a pact without the US, MarketWatch reported.
Haguida told a news conference that "without the US, it would lose the fundamental balance of benefits", MarketWatch said.
Chile's foreign minister Heraldo Munoz told a news conference that while another regional trade deal might be possible, "it wouldn't be the TPP", Reuters reported.
Chile has invited ministers from other TPP members as well as China and South Korea to a summit in March to discuss the situation, Reuters said.
There was no immediate statement from Canadian prime minister Justin Trudeau.
Sydney-based Margaret Cole of Pinsent Masons, the law firm behind Out-Law.com said: "The TPP as originally envisaged cannot proceed without the participation of the US. While the TPP may form the basis for an alternative trade agreement, we do not know to what extent other members were willing to sign up to the pact because of the participation of the US. From reported statements it seems likely that at least some members of the TPP fall into this category."
"As a result it seems likely there will be a complete reconsideration of the appropriate form for a Pacific trade agreement," she said. "While the TPP was at least in part motivated by the perceived need to provide a counterbalance to China, we may find that China is a participant in the new discussions. It also remains to be seen whether initial implementation steps for the TPP in Australia, such as the relaxation of foreign investment screening thresholds, will be reversed."
Bryan Tan of Pinsent Masons MPillay, the Singapore joint venture partner of Pinsent Masons, said: "Any treaty represents a balance of benefits and obligations, whether from a political, geopolitical and economic point of view. Each of the parties signing up to the original TPP must have already completed their calculations and decided that the TPP with the US would have net benefits for it. With the US now deciding that the TPP has insufficient benefits for it, it is surely for the other countries to go back to their capitals for re-calculations no matter how good the principles of the TPP might seem."
"The choices faced by the countries would be whether to salvage parts of the TPP, or to look at the alternatives, which are not like for like replacements, such as the China-backed RCEP and the ESCAP-backed Framework Agreement for Cross-Border Paperless Trade," Tan said.
"Many of the TPP countries have existing economic partnerships with the US and entering into the TPP could be seen as an extension of that relationship. If, as a result of these developments, new partnerships be created, these could pose challenges to any future bilateral arrangements the US seeks to have and also possibly lead to renegotiation of the existing partnerships," he said.
"The bigger picture issues are the signals being given by the abandonment of the TPP – that there will be disengagement with Asia. The Chinese have a saying – each mountain can only have one tiger. When the one tiger on the mountain decides to leave, other tigers will look to take its place. There are interested ‘tigers’ already circling this mountain and take over what has taken decades to build. The US should be careful that its signals do not get interpreted as a disengagement with Asia, if that is not its intention," Tan said.