"We're gonna have plenty of trade - but TPP wasn't the right way so we're going back to those countries, one on one, and that'll be beautiful."
The US already has free trade agreements with five of the other signatories: Canada, Mexico, Chile, Peru, and Singapore.
The five with which the US does not have FTAs are: Japan, New Zealand, Vietnam, Malaysia and Brunei.
New Zealand Trade Minister Todd McClay says trade ministers from TPP countries will meet in the coming months to discuss the future of the agreement.
"The US position is disappointing but not unexpected as the President Trump's views have been clear for some time," McClay said.
The cabinet, which is meeting today for the first time this year, is expected to be briefed on developments and next steps. Prime Minister Bill English will comment later today.
McClay said in a statement New Zealand's preference was to have US involved in the TPP.
"However, the agreement still has value as an FTA with the other countries involved."
For example, TPP was New Zealand's first FTA with Japan, Canada, Mexico, and Peru.
A number of TPP countries had expressed a strong commitment to the agreement, including Japan which has ratified.
McClay returned at the weekend from a trip to Europe during which he accompanied English to discuss imminent trade negotiations with the EU. He also attended the annual World Economic Forum summit in Davos.
"I met with a number of TPP Ministers in Davos last week and will continue to talk with them. I expect TPP ministers to meet over the next few months to consider how to move forward."
Trump also told the unions: "We are going to put a lot of people back to work. We are going to use common sense. We are going to do it the way it is supposed to be done.
"We are going to stop the ridiculous trade deals that have taken everybody out of our country and taken companies out of our countries. It is going to reversed."
He said it was "inconceivable" to him that it was allowed to happen in the first place.
"I am not blaming President Obama for this. I am blaming many, many years long beyond Obama. This has been going on for decades and it is a trend we are going to stop cold."
Trade specialist and advocate Stephen Jacobi expected that New Zealand would respond quickly and positively to an approach from the US for a bilateral.
"I think if they came and asked for a bilateral discussion I'm sure they will get on the plane ASAP."
He said it would not be a divide-and-rule approach because it would be possible for other countries to have new bilateral agreements with the United States and to continue with the TPP without the US.
That would require the remaining 11 TPP parties to amend the agreement, including the provision of what it would take for it to enter into force. The way it is currently worded, it could not enter into force without the United States.
But if the US has withdrawn as a signatory to the agreement, its consent would not be required to amend it.
Jacobi said the next steps for New Zealand would be to establish links with the new Administration to see what the US wanted to do bilaterally, and then for the other 11 to amend the agreement to proceed without the US but to "renegotiate as little as possible."
"I don't see any conflict in running TPP on the one hand with the 11 and building the bridge with the United States."
The US joined the TPP in 2008 under US President George W Bush.
It was then adopted as the primary trade initiative of President Barack Obama and was concluded in October 2015 but Obama did not put it to Congress for approval before he left office on January 20.
Japan and New Zealand have both completed changes to their domestic legislation which would take effect if the TPP entered into force.
Here is the wording of the directive (courtesy of Politico):
MEMORANDUM FOR THE UNITED STATES TRADE REPRESENTATIVE
SUBJECT: Withdrawal of the United States from the Trans-Pacific Partnership Negotiations and Agreement.
It is the policy of my Administration to represent the American people and their financial well-being in all negotiations, particularly the American worker, and to create fair and economically beneficial trade deals that serve their interests.
Additionally, in order to ensure these outcomes, it is the intentions of my Administration to deal directly with individual countries on a one-on-one (or bilateral) basis in negotiating future trade deals.
Trade with other nations is, and always will be, of paramount importance to my Administration and to me, as President of the United States.
Based on these principles, and by the authority vested in me as President by the Constitution and laws of the United States of America, I hereby direct you to withdraw the United States as a signatory to the Trans-Pacific Partnership (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.
You are directed to provide written notification to the Parties and to the Depository of the TPP, as appropriate, that the United States withdraws as a signatory of the TPP and withdraws from the TPP negotiating process.
You are authorized and directed to publish this memorandum in the Federal Register.
Donald J. Trump