The more positive environment came as concerns over Russia subsided following an aborted uprising, though developments in the nuclear-armed country are being closely followed as President Vladimir Putin faces the biggest test of his rule.
Sentiment was also boosted by comments from Chinese Premier Li Qiang on Tuesday, who said the government would roll out fresh measures to kickstart the nation's struggling economy and boost domestic demand.
With the events in eastern Europe a little less worrying for now, focus has returned to the battle against surging inflation, which has dogged global markets this year.
Last week's warning from US Federal Reserve chief Jerome Powell that rates would likely need to go higher dealt a blow to hopes that officials were at the end of close to completing their tightening cycle.
While the Fed stood pat this month, his comments came as central banks elsewhere continued to push borrowing costs higher and indicated more were in the pipeline.
The Fed said the decision at the next policy meeting at the end of July will be determined by incoming data, putting the focus on upcoming releases, including Friday's personal consumption expenditures (PCE) index -- the central bank's preferred measure of inflation.
But analysts warned that investors face more pain this year, while there is a growing concern that the tightening could tip economies into recession, as has happened in the eurozone.
"I'm not sure we have felt the full effect of the whole inflation cycle," Nancy Daoud, at Ameriprise Financial Services, told Bloomberg Television.
"Those rate hikes are very, very likely in July and in early fall."
Most Asian markets rose, brushing off losses on Wall Street.
Hong Kong climbed almost two percent after five days of losses, while Shanghai, Sydney, Singapore, Wellington, Mumbai and Bangkok also rose.
Tokyo, Seoul, Manila, Jakarta and Taipei retreated.
London, Paris and Frankfurt also rose in the morning.
- Russia worries -
China's Li also told global political and business leaders at the World Economic Forum in northern China that the country would achieve its five percent growth target this year.
His remarks came after markets were left disappointed when officials failed to provide details of a hoped-for raft of stimulus measures, while interest rate cuts by the Chinese central bank provided only a brief lift.
Oil rose again though traders remain caught between supply concerns caused by the Russia crisis and demand uncertainty as investors fret over surging interest rates.
And the ruble held losses after weakening to levels not seen since the early months of Putin's invasion of Ukraine, with a wary eye still being kept on developments in Moscow.
Putin on Monday accused Ukraine and its Western allies of wanting Russians to "kill each other" during the revolt by mercenaries from Yevgeny Prigozhin's Wagner group.
Prigozhin earlier defended the mutiny as a bid to save his fighters and expose the failures of Russia's military leadership over the Ukraine war -- but not to challenge the Kremlin.
US National Security Council spokesman John Kirby said officials were monitoring events "very closely".
Meanwhile, in a fresh sign of optimism for China-US relations, reports said Treasury Secretary Janet Yellen planned to meet her counterpart in Beijing next month.
The talks would come soon after Secretary of State Antony Blinken's trip to the country, where he spoke to his opposite number and President Xi Jinping. A summit between Xi and President Joe Biden has also been flagged.
- Key figures around 0810 GMT -
Tokyo - Nikkei 225: DOWN 0.5 percent at 32,538.33 (close)
Hong Kong - Hang Seng Index: UP 1.9 percent at 19,148.13 (close)
Shanghai - Composite: UP 1.2 percent at 3,198.44 (close)
London - FTSE 100: UP 0.2 percent at 7,471.29
Euro/dollar: UP at $1.0941 from $1.0910 on Monday
Pound/dollar: UP at $1.2738 from $1.2714
Dollar/yen: DOWN at 143.47 from 143.50 yen
Euro/pound: UP at 85.89 pence from 85.78 pence
West Texas Intermediate: UP 0.5 percent at $69.71 per barrel
Brent North Sea crude: UP 0.4 percent at $74.51 per barrel
New York - Dow: DOWN less than 0.1 percent at 33,714.71 (close)
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