SINGAPORE - Global markets greeted Donald Trump's presidency with apprehension on Tuesday in moves that were highly sensitive to headlines over the newly sworn-in president's plans for trade relations and tariffs in particular.

US markets were closed for a holiday on Monday, so the first reactions to Trump's return to the White House were felt during Asian trade on Tuesday, with European futures also pointing to a lower open.

Just as investors cheered the possibility of a delay in Trump's implementation of tariffs following a brief mention of the topic in his inauguration speech, the US president said shortly after that he was mulling imposing 25 percent tariffs on Mexico and Canada as soon as Feb 1.

That sent the Mexican peso sliding 1 percent against the dollar while the Canadian dollar tumbled to a five-year low of C$1.4515.

Trump also said he wanted to reverse the US trade deficit with the European Union, either with tariffs or more energy exports.

European carmakers will be in focus after Trump revoked a 2021 executive order signed by his predecessor that sought to ensure half of all new vehicles sold in the United States by 2030 were electric.

Trump's tariff comments quickly reversed gains in global stock markets and sent the greenback rebounding strongly across the board in choppy trade.

"The first few hours of the Trump administration have underscored that the policy environment will be dynamic once again and markets should brace for volatility," said Charu Chanana, Saxo's chief investment strategist.

"Clearly, the markets celebrated too soon with tariff threats missing at the outset in Trump's inaugural speech."

US stock futures pared their strong gains from earlier in the session, leaving Nasdaq futures flat and S&P 500 futures 0.1 percent higher.

Japan's Nikkei similarly swung between losses and gains and was last up 0.13 percent.

Trump's plans for hefty import tariffs have been a key area of focus for financial markets on the view that such policies will stoke inflation and run the US economy red hot again, which would boost the dollar and hurt bonds.

Some investors had expected a swift imposition of tariffs from the moment he took office, so the lack of any concrete moves initially sparked a brief relief rally across stocks and US Treasuries.

"At some point, we are quite certain that Trump will start to move on the tariff measures ... It's quite clear what his intent is," said Khoon Goh, head of Asia research at ANZ.

"The fact that he hasn't addressed this on day one doesn't mean that it is off the agenda. It is definitely firmly on the agenda, it's just that we have to wait and see what shape or form he takes."

The benchmark 10-year US Treasury yield was last 7.1 basis points lower at 4.54 percent. Yields move inversely to bond prices.

In currencies, the dollar clawed back its losses from earlier in the session and distanced itself from a two-week low.

The euro slid 0.3 percent to $1.0385, while sterling weakened 0.32 percent to $1.2290.

MSCI's broadest index of Asia-Pacific shares outside Japan was up 0.34 percent.

Trump's new crypto token gave up some of its strong gains on Tuesday to fall 20 percent to $35.27, after having soared to more than $10 billion in market value at the start of the week.

Bitcoin dipped 0.08 percent to $102,460.68, easing away from a record high hit on Monday.

The prospect of looser regulations around crypto policy under the Trump administration has been met with fanfare by the industry and turbocharged a rally across digital assets following his election victory in November.

In commodities, oil prices were little changed as investors digested Trump's plan to maximize US oil and gas production by declaring a national emergency.

Brent crude futures were flat at $80.1 a barrel, near its lowest in more than a week. US West Texas Intermediate crude futures fell 0.8 percent to $77.24 per barrel from Friday's close. There was no settlement on Monday due to a US public holiday.