A report saying the incoming US leader's economics team was considering slowly hiking tariffs on imports provided support to traders and put a cap on the dollar's latest surge, while news of fresh curbs on AI chips to China appeared to have little immediate impact.
However, traders remain concerned that his pledges to cut taxes, regulations and immigration continue to dampen sentiment with warnings that the measures will revive inflation.
Traders have slashed their expectations on how many times the Federal Reserve will cut interest rates through 2025 to one, from four predicted last year, while there is even talk that the next move could be a hike owing to still-sticky inflation and Trump concerns.
Data on Friday showing the world's top economy created far more jobs than forecast in December dealt yet another blow to the chances of another reduction at the Fed's next meeting and sent equity markets deep into the red.
Wall Street staged a small recovery Monday, with the Dow and S&P ending in positive territory, but tech titans including big-hitter Nvidia dragged the Nasdaq down again.
Asian markets fluctuated in the morning.
Hong Kong, Shanghai, Sydney, Wellington, Taipei and Jakarta rose, though there were losses in Singapore, Manila and Seoul, with Tokyo the biggest loser as traders returned from a long weekend to play catch-up with Monday's sell-off.
The dollar eased back against its peers after Bloomberg reported that members of Trump's team were looking at a gradual increase in tariffs in a bid to boost their negotiating hand and tamper inflationary pressures.
Traders were spooked when he said soon after his re-election that he would impose huge levies on China, Canada and Mexico as soon as he took office.
But while the dollar eased, the pound remained stuck at levels not seen since the end of 2023. The euro was near its weakest since late 2022, with fears it could return to parity with the dollar.
Eyes are now on the release of US inflation data this week and the beginning of the release of corporate reports.
"This earnings season will set the tone for financial stocks in 2025, but the stakes are high," said Charu Chanana, chief investment strategist at Saxo Markets.
"Even with solid fourth-quarter results, the macro backdrop -- characterised by lingering inflation concerns, steeper yields, and recalibrated Fed expectations -- may weigh on sentiment.
"With valuations already elevated after a strong 2024, further stock gains will require more than just decent earnings. Robust outlooks, ongoing loan demand, and resilient consumer credit will be critical to sustaining investor confidence."
She added that "uncertainty around Fed policy and a potential shift in fiscal priorities under Trump's new administration will keep markets on edge".