The new U.S. president made good on one of his campaign promises Monday, formally withdrawing the United States from the Trans-Pacific Partnership free-trade deal, and signalling his intention to renegotiate NAFTA "at the appropriate time."

Calling the move "great news for American workers," Donald Trump signed an executive order pulling the U.S. out of TPP, a pan-oceanic trade pact signed by his predecessor but never ratified.

The 12-nation trade deal had been a target of his wrath on the campaign trail. "We are going to stop the ridiculous trade deals that have taken everybody out of our country and taking companies out of our country," Trump said after signing the order.

Prominent Republican — and frequent Trump critic — Senator John McCain of Arizona was quick to criticize the decision, releasing a statement calling it a "serious mistake."

"This decision will forfeit the opportunity to promote American exports, reduce trade barriers, open new markets and protect American invention and innovation," McCain said. "It will create an opening for China to rewrite the economic rules of the road."

On the other side of the political aisle, Vermont Senator and erstwhile presidential candidate Bernie Sanders cautiously welcomed the move.

"I am glad the Trans-Pacific Partnership is dead and gone. For the last 30 years, we have had a series of trade deals — including the North American Free Trade Agreement ... which have cost us millions of decent-paying jobs and caused a 'race to the bottom,' which has lowered wages for American workers," Sanders said.

"Now is the time to develop a new trade policy that helps working families, not just multi-national corporations. If President Trump is serious about a new policy to help American workers then I would be delighted to work with him."

NAFTA questioned too

Reports Monday suggested the Trump administration would also sign an order to formally attempt to renegotiate NAFTA. While that didn't come to pass, Trump told reporters that discussions on the future of the North American Free Trade Agreement would begin "at the appropriate time."

At a press briefing later on Monday, White House press secretary Sean Spicer said no further executive orders are planned today, but more movements on trade are expected later this week.

An adviser to the Trump White House said Monday that there's a "very low risk" of Canada suffering any "collateral damage" in any NAFTA discussions.

At last count, at least 35 U.S. states counted Canada as their largest trading partner, and those states won't want to see the border thicken in either direction.

Nations with which the U.S. has a trade deficit will be more of an area of focus, said Blackstone Group CEO Stephen Schwarzman, head of a group of business leaders who are advising Trump on economic matters.

Spicer said exiting the TPP is a symbol of a "new era" of U.S. trade policy.

"This type of multinational agreement is not in our best interest," Spicer said, adding that the administration favours one-on-one bilateral trade deals.

"The president's vision is to negotiate trade deals that create American jobs."

Spicer added that the president is open to renegotiating NAFTA in its current structure, and expects those talks to begin within the next month. But he added that if that's not possible the administration will pursue new bilateral deals.