Investors were back in a buying mood after last week's ructions caused by Donald Trump's threat earlier in the month to hammer China with 100 percent tariffs over its latest rare earth export controls.

The US president -- who had lashed Beijing's "extraordinarily aggressive" moves -- has since toned down his rhetoric and on Monday expressed optimism ahead of a meeting with Chinese counterpart Xi Jinping at the APEC summit in South Korea.

He said he was focused on getting a "fair" trade deal between the superpowers, adding: "I want to be good to China. I love my relationship with President Xi. We have a great relationship."

He also said he doubted China would invade Taiwan, saying, "I think we'll be just fine with China. China doesn't want to do that."

The remarks, which followed other conciliatory words at the weekend, helped push Wall Street higher, as the tech-led rally that has pushed markets to records got back on track.

"Markets are travelling on 'high hopes' for a thaw in US-China relations, with President Trump listing rare earths, fentanyl and soybeans as top issues ahead of trade talks," said National Australia Bank's Rodrigo Catril.

Hong Kong and Shanghai jumped more than one percent, while Singapore, Sydney, Seoul, Taipei, Manila, Bangkok and Jakarta were also well in positive territory, along with London and Frankfurt. Paris was flat.

Tokyo's early surge was pared by the Nikkei 225 ended at a new high, following Monday's 3.4 percent surge, as Japan's first woman prime minister was appointed, after Sanae Takaichi reached a deal to form a new coalition.

The agreement eased worries about political strife in the country after the Komeito party withdrew from its long-standing alliance with Takaichi's Liberal Democratic Party soon after her election.

Markets have been cheered by the prospect of her premiership as she has in the past backed aggressive monetary easing and expanded government spending, echoing her mentor, former premier Shinzo Abe.

"Markets are focused on the fiscal deficit impact of the budget; excessive measures could trigger a Japan sell-off, while insufficient measures may unwind the Takaichi trade," said Masamichi Adachi at UBS.

Traders are also keeping tabs on Beijing, where China's leaders are holding a four-day conclave expected to discuss strategies to address sluggish household spending and persisting woes in the vast property sector.

The gathering comes after data Monday showed growth in the world's number two economy came as expected for the third quarter, but was the slowest in a year.

Mineral producers fell in Sydney, having opened sharply higher following a deal between Trump and Australian Prime Minister Anthony Albanese to ramp up shipments of rare earths to the United States.

Hastings Technology Metals, Lynas Rare Earths and Iluka Resources all surged at the open but gave up their gains as the day wore on and ended in the red.

- Key figures at around 0715 GMT -

Tokyo - Nikkei 225: UP 0.3 percent at 49,316.06 (close)

Hong Kong - Hang Seng Index: UP 1.3 percent at 26,185.59

Shanghai - Composite: UP 1.4 percent at 3,916.33 (close)

London - FTSE 100: UP 0.3 percent at 9,428.31

Euro/dollar: DOWN at $1.1632 from $1.1641 on Monday

Pound/dollar: DOWN at $1.3390 from $1.3409

Dollar/yen: UP at 151.33 yen from 150.73 yen

Euro/pound: UP at 86.87 percent from 86.82 pence

West Texas Intermediate: UP 0.1 percent at $57.57 per barrel

Brent North Sea Crude: FLAT at $61.00 per barrel

New York - Dow: UP 1.1 percent at 46,706.58 (close)

dan/lb

NATIONAL AUSTRALIA BANK

ILUKA RESOURCES

INDEX CORP.

Dow