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.

Takaichi also said Japan was facing an "unprecedented severe security environment", in a nod to the geopolitical tensions underlying Trump's Asia tour.

Japan's Nikkei 225 index finished the day down 0.6 percent, after surging above 50,000 points on Monday for the first time.

Shares in Hong Kong, Shanghai, Taipei and Sydney also slid, while Seoul rallied from a more than one percent drop to close down 0.8 percent.

Morning trading in Europe saw shares edge up in London, while Paris and Frankfurt were down.

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.

Oil prices fell by more than one percent Tuesday after a report said that the Opec+ group is leaning towards a production boost in December.

- Key figures at around 0820 GMT -

Tokyo - Nikkei 225: DOWN 0.6 percent at 50,219.18 (close)

Hong Kong - Hang Seng Index: DOWN 0.3 percent 26,346.14 (close)

Shanghai - Composite: DOWN 0.2 percent at 3,988.22 (close)

London - FTSE 100: UP 0.1 percent at 9,665.30

West Texas Intermediate: DOWN 1.3 percent at $60.50 per barrel

Brent North Sea Crude: DOWN 1.3 percent at $64.74 per barrel

Euro/dollar: UP at $1.1657 from $1.1646 on Monday

Pound/dollar: DOWN at $1.3332 from $1.3333

Dollar/yen: DOWN at 152.04 yen from 152.90 yen

Euro/pound: UP at 87.44 from 87.35 pence

New York - Dow: UP 0.71 percent at 47,544.59 (close)