Attention is also on meetings by major central banks, with Japan announcing a small tweak to its policy control programme that fell short of expectations, sending the yen down against the dollar but providing support to the country's equity market.
There is a sense of relief on trading floors that the Israel-Hamas conflict has not geographically spread to include other regional powers such as Iran or Saudi Arabia so far, analysts say.
After surging almost three percent Friday on fears of a wider conflagration, both main oil contracts tumbled more than three percent at the start of this week as Israel opted for more day-to-day attacks targeting Gaza.
While Israeli Prime Minister Benjamin Netanyahu has ruled out a ceasefire, Yeap Jun Rong at IG Asia said there were market "expectations that the conflict may still be contained".
Israel's intensifying land and air campaign since Hamas's October 7 attacks has heightened fears for the 2.4 million civilians trapped inside Gaza, where the Hamas-ruled health ministry says more than 8,300 have been killed by Israeli bombardment.
Tel Aviv says more than 1,400 people, mainly civilians, were killed in Israel -- most of them on October 7 -- with more than 230 people taken hostage.
With worries about supplies from the crude-rich Middle East subsiding for now, both main oil contracts clawed back only some of Monday's losses in Asia.
The mood was a little less cheery on stock markets, even after a rally on Wall Street.
Data showing China's factory sector activity shrank in October weighed on sentiment, dragging on Hong Kong and Shanghai on fresh worries about the world's number-two economy.
"Market confidence in the Chinese economy remains depressed, with continued capital outflows," said Nomura analysts including Ting Lu.
"We expect economic conditions to remain poor or even to deteriorate further in coming months."
There were also losses in Seoul, Taupei, Mumbai, Bangkok and Jakarta but Sydney, Singapore, Wellington and Manila rose.
Tokyo reversed from morning losses after the Bank of Japan said it would "conduct yield curve control (YCC) with the upper bounds of 1.0 percent for those yields as a reference".
Speculation had been swirling that officials were talking about further widening the band in which it allows bond yields to move.
YCC has helped keep monetary policy ultra-loose as the BoJ tries to stimulate the economy, even as the Fed pushed borrowing costs to two-decade highs. The moves have seen the yen tumble this year and led to talk of an intervention by authorities.
The yen weakened to more than 150 per dollar Tuesday after the announcement, having moved towards 149 the day before on reports of a change of tack.
Still, Stephen Innes at SPI Asset Management said that "regardless of this less hawkish outcome than some corners of the market thought, the signal is they are close to shifting policy, which could limit yen's weakness".
- Key figures around 0705 GMT -
Tokyo - Nikkei 225: UP 0.5 percent at 30,858.85 (close)
Hong Kong - Hang Seng Index: DOWN 1.5 percent at 17,141.31
Shanghai - Composite: DOWN 0.1 percent at 3,018.77 (close)
Dollar/yen: UP at 150.21 yen from 149.06 yen on Monday
Euro/dollar: DOWN at $1.0609 from $1.0619
Pound/dollar: DOWN at $1.2150 from $1.2168
Euro/pound: UP at 87.31 pence from 87.23 pence
West Texas Intermediate: UP 0.9 percent at $83.02 per barrel
Brent North Sea crude: UP 1.0 percent at $88.31 per barrel
New York - Dow: UP 1.6 percent at 32,928.96 (close)
London - FTSE 100: UP 0.5 percent at 7,327.39 (close)
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