Asian stocks were mixed Tuesday as some stability returned to markets after last week's rollercoaster ride, with auto firms boosted by Donald Trump's possible compromise over steep tariffs on the sector.

However, the US president's unorthodox approach to trade diplomacy continues to fuel uncertainty among investors, with speculation over new levies on high-end technology and pharmaceuticals dampening sentiment.

The announcement last week of exemptions for smartphones, laptops, semiconductors and other electronics — all key Chinese-made products — provided a little comfort, though Trump's suggestion they would be temporary tempered the optimism.

Traders gave a muted reaction to Treasury Secretary Scott Bessent's remarks Monday that a China-US deal could be done in an apparent olive branch as the two economic powerhouses trade tariff threats.

His comments came as Trump has hammered China with duties of up to 145 percent, while Beijing has imposed retaliatory measures of 125 percent.

"There's a big deal to be done at some point" Bessent said when asked by Bloomberg TV about the possibility that the world's largest economies would decouple. "There doesn't have to be" decoupling, he said, "but there could be."

Meanwhile, Trump aide Kevin Hassett said the White House had received "more than 10 deals where there's very, very good, amazing offers made to us", but did not specify which countries.

After a broadly positive day on Wall Street, Asian markets fluctuated.

Tokyo and Seoul were among the best performers thanks to a rally in autos after Trump said he was "very flexible" and "looking at something to help some of the car companies" hit by his 25 percent tariff on all imports.

Toyota and Mazda jumped five percent and Nissan more than three percent, while Seoul-listed Hyundai jumped more than four percent.

South Korea's announcement of plans to invest an additional $4.9 billion in the country's semiconductor sector gave a little lift to chip giants Samsung and SK hynix.

Sydney, Singapore, Taipei, Manila and Jakarta also rose. Hong Kong and Shanghai dipped with Wellington.

Federal Reserve governor Christopher Waller provided some support to markets after suggesting he would back the central bank to cut interest rates to help the economy, instead of focusing on higher inflation.

He pointed out that prices could see a transitory rise because of the tariffs but added that if Trump reverted to the crippling tariffs included in his "Liberation Day" on April 2 then officials would be ready to step in.

"If the slowdown is significant and even threatens a recession, then I would expect to favor cutting the... policy rate sooner, and to a greater extent than I had previously thought," he said in comments prepared for an event Monday. 

"In my February speech, I referred to this as the world of 'bad news' rate cuts. With a rapidly slowing economy, even if inflation is running well above two percent, I expect the risk of recession would outweigh the risk of escalating inflation, especially if the effects of tariffs in raising inflation are expected to be short lived."

However, OANDA senior market analyst Kelvin Wong warned central bankers would face some tough choices.

"Combination of slowing growth and persistent inflation, hallmarks of a stagflation environment, poses a significant challenge for the US Federal Reserve, which may find it increasingly difficult to implement counter-cyclical monetary policies to support the economy," he said in a commentary.

Key figures around 0230 GMT

Tokyo - Nikkei 225: UP 0.9 percent at 34,285.02 (break)

Hong Kong - Hang Seng Index: DOWN 0.2 percent at 21,379.50

Shanghai - Composite: DOWN 0.3 percent at 3,254.04

Dollar/yen: UP at 143.32 yen from 143.09 yen on Monday

Euro/dollar: DOWN at $1.1327 from $1.1356 

Pound/dollar: DOWN at $1.3179 from $1.3189

Euro/pound: DOWN at 85.94 pence from 86.08 pence

West Texas Intermediate: UP 0.3 percent at $61.69 per barrel

Brent North Sea Crude: UP 0.2 percent at $65.03 per barrel

New York - Dow: UP 0.8 percent at 40,524.79 (close)

London - FTSE 100: UP 2.1 percent at 8,134.34