In a much-anticipated speech via video link at the Davos World Forum in Switzerland, Trump pushed for lower interest rates and said he would cut taxes for companies investing in the United States while imposing tariffs on those who do not.
He also called on Saudi Arabia and OPEC to lower oil prices, adding that "when the oil comes down, it'll bring down prices" and in turn bring interest rates down.
His comments come after he said on the campaign trail that he would slash taxes, regulations and immigration while hitting key trading partners with tariffs.
That fuelled worries among some economists that he could reignite inflation and cause the Federal Reserve to pause its recent run of rate cuts, or even increase them.
US traders appeared to welcome the speech, with the S&P 500 hitting a record high, while the Dow and Nasdaq also advanced.
Asia mostly followed suit, with Hong Kong, Shanghai, Sydney, Seoul, Mumbai and Bangkok all up, though Tokyo, Singapore, Wellington, Jakarta and Manila slipped.
London and Frankfurt rose again after hitting fresh record highs Thursday, while Paris also advanced.
Markets have enjoyed a broadly positive start to Trump's second term amid relief that while he has warned about imposing big tariffs on key partners, he has so far been less abrasive than his first four years.
Matt Burdett and Adam Sparkman at Thornburg Investment Management said that could be due to circumstances.
"Eight years ago, Trump's aggressive trade policies were implemented against a backdrop of low inflation and low rates, creating room for bold actions," they said in a commentary.
"Today, elevated price levels are a key concern for voters and policymakers alike. Given this reality, we question if Trump's tariff posturing may now be aimed more at pressuring China and other foreign countries into negotiating favourable trade terms for the US."
- Japan hikes rates -
The Bank of Japan on Friday lifted borrowing costs to their highest level since 2008 in a well-telegraphed move, with data showing another jump in inflation last month that reinforced expectations for further tightening.
"Japan's economic activity and prices have been developing generally in line with the Bank's outlook, and the likelihood of realising the outlook has been rising," the bank said in a statement.
The yen briefly rallied to as strong as 154.85 per dollar after officials flagged more increases were likely in the pipeline as inflation remains elevated and officials slowly withdraw stimulus that has kept monetary policy at ultra-loose levels for years.
Moody's Analytics said "the weak yen is a key reason" for the hike, along with a run of forecast-beating inflation prints.
BoJ chief Kazuo Ueda told a news conference that the pace and timing of future hikes was yet to be determined.
"We would like to make a decision after we have studied the impact of this rate hike," he said.
The yen has come under pressure against the dollar in recent months after the Fed dialled back its expectations for rate cuts this year and the concerns over Trump's impact on inflation.
The BoJ decision comes ahead of the Fed's meeting next week, which will be closely watched for its views on the outlook under the new president.
Oil prices were barely moved after Thursday's losses that followed Trump's call to Riyadh and OPEC, with a recent build in US stockpiles adding to the weakness.
- Key figures around 0815 GMT -
Tokyo - Nikkei 225: DOWN 0.1 percent at 39,931.98 (close)
Hong Kong - Hang Seng Index: UP 1.9 percent at 20,066.19 (close)
Shanghai - Composite: UP 0.7 percent at 3,252.63 (close)
London - FTSE 100: UP 0.2 percent at 8,585.56
Dollar/yen: DOWN at 155.39 yen from 156.03 yen on Thursday
Euro/dollar: UP at $1.0461 from $1.0415
Pound/dollar: UP at $1.2385 from $1.2352
Euro/pound: UP at 84.46 pence from 84.31 pence
West Texas Intermediate: DOWN 0.1 percent at $74.57 per barrel
Brent North Sea Crude: FLAT at $78.28 per barrel
New York - Dow: UP 0.9 percent at 44,565.07 (close)
dan/dhw
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