The US president is due to meet Xi Thursday in South Korea, and rosy comments by Trump have fuelled optimism that the world's two largest economies can strike a deal to ease their trade war.
Those hopes spurred stocks to record highs Monday on Wall Street, where investors are also preparing for earnings reports from tech giants including Microsoft and Meta this week.
In Tokyo on Tuesday, Trump met new Japanese Prime Minister Sanae Takaichi, declaring that the United States was "an ally at the strongest level".
The White House announced that the countries had signed an agreement on the supply of rare earths, a critical sector dominated by China that has deepened the antipathy between Washington and Beijing.
Japan's Nikkei 225 index pared back gains early Tuesday after surging above 50,000 points for the first time the previous day.
Shares in Hong Kong and Sydney also recorded gentle drops, while Seoul fell by more than one percent.
Taipei stocks were up slightly, while Shanghai was flat.
The strong start to the week on Wall Street was "driven by news that the United States and China were set to forge some sort of trade agreement", wrote Chris Weston of Pepperstone in a note.
"There seems little in the global macro landscape that appears capable of derailing the current melt-up," he wrote, adding that an absence of US economic data in the midst of a continuing government shutdown is "limiting" risk.
The buoyant mood has been defying tumultuous trade tensions between Beijing and Washington, with a looming threat by Trump to impose further blistering tariffs on China from November 1, though the US leader later tempered his statement.
Speaking before arriving in Japan on Monday, Trump said he was hopeful of a deal with Xi, whom he will meet on the sidelines of the Asia-Pacific Economic Cooperation summit in their first face-to-face meeting since the US leader returned to office.
Key Chinese trade negotiator Li Chenggang said Sunday a "preliminary consensus" with the United States had been reached.
- Key figures at around 0230 GMT -
Tokyo - Nikkei 225: DOWN 0.4 percent at 50,287.81
Hong Kong - Hang Seng Index: DOWN 0.1 percent 26,397.12
Shanghai - Composite: FLAT at 39,98.28
West Texas Intermediate: FLAT at $61.31 per barrel
Brent North Sea Crude: UP 0.1 percent at $65.66 per barrel
Euro/dollar: UP at $1.1658 from $1.1646 on Monday
Pound/dollar: UP at $1.3355 from $1.3333
Dollar/yen: DOWN at 152.42 yen from 152.90 yen
Euro/pound: DOWN at 87.30 from 87.35 pence
New York - Dow: UP 0.71 percent at 47,544.59 (close)
London - FTSE 100: UP 0.1 percent at 9,653.82 (close)
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