Most Asian and European markets fell Tuesday and the dollar rose as fresh fears that the US Federal Reserve will push interest rates higher than hoped overshadowed growing optimism over China's economic reopening.

After a strong start to the week in Asia, traders tracked a big drop on Wall Street that came on the back of data showing a forecast-busting jump in activity in the US services sector last month.

The news -- combined with Friday's bigger-than-expected print on November jobs and wage increases -- dented optimism that the Fed's monetary tightening campaign was finally paying off, which would give it room to take a less hawkish approach into the new year.

Markets had been running higher ahead of the jobs figures after a surprise drop in inflation and comments from Fed boss Jerome Powell that the bank would likely raise rates at a slower pace.

"Outstanding news from the vast services-based US economy is devastating for market participants keen to see evidence of the US economic disintegration," said SPI Asset Management's Stephen Innes.

"Coming as it did on the heels of Friday's jobs report, which indicated that the rumours of the US economic demise were greatly exaggerated, the market immediately moved into 'good news is bad' mode, which saw investors ride roughshod over the dovish pivot camp."

Bets have increased on borrowing costs going higher than five percent next year -- from the current 3.75 to 4.0 percent -- before the bank pauses, with no cuts seen until 2024.

All three main indexes on Wall Street lost more than one percent and Asia struggled to maintain its recent momentum.

Hong Kong dropped after soaring around 15 percent over the past week on China's easing of strict Covid containment measures.

Sydney, Seoul, Singapore, Wellington, Mumbai, Bangkok, Taipei and Jakarta were also in the red.

Shanghai was barely moved while Tokyo rose. Manila was up more than three percent as banks were boosted by a forecast-beating jump in inflation that ramped up expectations for a hike in interest rates.

London, Paris and Frankfurt all slipped at the open.

The dollar extended most of the gains made Monday after the services data release. The Australian dollar was among the biggest losers after the country's central bank lifted interest rates to a decade high but by less than expected.

The mood in Asia remains largely positive owing to the prospect of China rolling back some of the harsh measures that have been in place for almost three years and have hammered the giant economy.

But analysts said the country would not likely see a complete end to the zero-Covid policy for several months.

Oil prices climbed Tuesday, having dropped heavily the two previous days, on expectations that a reopening will boost demand in the world's biggest importer of the commodity.

- Key figures around 0820 GMT -

Tokyo - Nikkei 225: UP 0.2 percent at 27,885.87 (close)

Hong Kong - Hang Seng Index: DOWN 0.4 percent at 19,441.18 (close)

Shanghai - Composite: FLAT at 3,212.53 (close)

London - FTSE 100: DOWN 0.1 percent at 7,562.19

Euro/dollar: DOWN at $1.0490 from $1.0495 on Monday

Dollar/yen: UP at 136.90 yen from 136.78 yen

Pound/dollar: UP at $1.2200 from $1.2186

Euro/pound: DOWN at 85.99 pence from 86.06 pence

West Texas Intermediate: UP 0.8 percent at $77.53 per barrel

Brent North Sea crude: UP 0.9 percent at $83.44 per barrel

New York - Dow: DOWN 1.4 percent at 33,947.10 (close)