The United States has formally pulled out of the Trans-Pacific Partnership (TPP) trade deal.

Acting US trade representative Maria Pagan has written to the TPP's secretariat office in Wellington saying the "United States does not intend to become a party to the Trans-Pacific Partnership agreement".

"Accordingly, the United States has no legal obligations arising from its signature on February 4, 2016," the letter says.

Pagan asked the secretariat to inform other signatories of the treaty -- namely, Australia, New Zealand, Canada, Singapore, Vietnam, Malaysia, Japan, Mexico, Peru, Brunei, and Chile.

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"The United States remains committed to taking measures designed to promote more efficient markets and higher levels of economic growth, both in our country and around the world," Pagan said.

"We look forward to further discussions as to how to achieve these goals."

The rejection of the TPP fulfils a campaign pledge from US President Donald Trump in an effort to return jobs to American shores under the auspices of an "America first" mantra.

"The president understands how critical it is to put American workers and businesses first when it comes to trade. With tough and fair agreements, international trade can be used to grow our economy ... this strategy starts by withdrawing from the Trans-Pacific Partnership and making certain that any new trade deals are in the interests of American workers," the White House said in a statement last week.

Alongside the TPP, the new administration has said it will also renegotiate the North American Free Trade Agreement (NAFTA), and has threatened to withdraw from the trilateral agreement with Mexico and Canada if American workers are not given a "fair deal".

Among the other signatories to the trade deal, some nations are looking to push ahead and legislate its terms despite the withdrawal of the nation making up 60 percent of the GDP covered by the agreement, while other countries are walking away or looking to alternative bilateral deals.

Japan has already ratified the deal, but it cannot come into force, as its terms state that at least six nations making up 85 percent of the GDP of the signatories must ratify it.

The executive order to leave the TPP was signed in the same week that the United States' 45th president signed an order banning citizens and dual-citizens of seven predominantly Muslim nations -- Syria, Iraq, Libya, Iran, Sudan, Somalia, and Yemen -- from entering the US. The order also placed a temporary hold on any refugees entering the US for 120 days.

Response to the order has seen protests, as well as condemnation from a number of foreign governments and affected large enterprises.

For its part, Microsoft said it is cooperating with the Washington State Attorney General's Office, which is suing in the Federal Court to stop Trump's immigration order.

Microsoft is providing information about the order's impact "in order to be supportive -- and we'd be happy to testify further if needed", spokesman Pete Wootton said in a statement.

CNN has reported that acting US Attorney General Sally Yates does not believe the immigration orders are lawful, and has directed Justice Department lawyers to not defend the orders against actions from a number of US states.

Australian Prime Minister Malcolm Turnbull refused to criticise the immigration order.

"It is not my job, as prime minister of Australia, to run a commentary on the domestic policies of other countries," Turnbull said in a press conference on Monday.

"If others wish to emulate what we're doing [with border control], they're welcome to do so, but I am not about to run a commentary on other countries' practices."

Despite Turnbull saying it was not aware of the ban impacting Australians with dual-citizenship from the seven nations, reports have emerged that such Australians have been stopped at airports before flights to the United States.

The prime minister announced on Tuesday morning that a deal is now in place to exempt Australian dual-nationals from the US immigration and travel ban.

"When I have frank advice to give to an American president, I give it privately, as good friends should, as wise prime ministers do, when they want to ensure they are best able to protect Australians and Australians' national interest," he told reporters in Canberra on Tuesday.

"Others can engage in commentary. My job is to stand up for Australia, Australian interests, and deliver, and that's what we've done today."

Shadow Attorney-General Mark Dreyfus cited a Facebook post by former US ambassador to Australia Jeffrey Bleich condemning the new administration.

Bleich took to social media to label the visa ban illegal and cruel, saying it violates the most basic tenets of the US.

"I take no pleasure in condemning our nation's actions," he wrote.

"But the hottest places in hell are reserved for those who, in times of great moral crisis, maintain their neutrality."

With AAP