Tokyo's Nikkei 225 index rose 1.8 percent to 21,362.60 and Hong Kong's Hang Seng gained 0.5 percent to 28,663.04. The Shanghai Composite Index was unchanged at 3,043.02 and Sydney's S&P-ASX 200 was flat at 6,126.50. Seoul's Kospi advanced 0.4 percent to 2,142.50 and benchmarks in New Zealand, Taiwan and Southeast Asia also rose.
On Monday, major markets in Europe and Asia tumbled as traders tried to make sense of pessimistic new outlooks on global growth.
On Wall Street, the benchmark Standard & Poor's 500 ended down 0.1 percent at 2,798.36 points. That added to losses from last week's sell-off.
Traders were rattled by a drop in long-term bond yields, which many see as a warning sign of a possible recession.
"Worries about global growth are evident," said Shane Oliver of AMP Capital in a report.
Despite that, "we see this year as being a decent year for share market returns," said Oliver. He pointed to a shift by central banks toward easier monetary policy, China's plans for economic stimulus and fading fears about the U.S.-Chinese tariff war.
European investors are uneasy about the uncertain outlook for Britain's plan to leave the European Union.
British lawmakers seized a measure of control over the process from Prime Minister Theresa May on Monday. That set up votes that could alter the course of Britain's departure from the European Union.
The move came after May conceded Parliament would defeat her twice-rejected divorce deal with the EU again if she put it to a third vote.
Worried investors have shifted money into bonds, sending yields lower. The yield on the 10-year U.S. Treasury slid to 2.40 percent from 2.45 percent late Friday. At one point, the yield had fallen to 2.38 percent, briefly triggering deeper declines in the stock indexes.
The 10-year Treasury yield is below the yield on the three-month Treasury bill, a worrying sign that in the past has preceded recessions. That occurred Friday.
APPLE TV: The company announced plans to launch a subscription TV service but failed to impress investors. Its stock slid 1.2 percent. The company did not say how much Apple TV Plus, which will be ad-free, will cost or when exactly it will debut. It will compete with big streaming services including Netflix and Amazon Video.
ENERGY: Benchmark U.S. crude gained 37 cents to $59.19 per barrel in electronic trading on the New York Mercantile Exchange. The contract shed 22 cents on Monday to close at $58.82. Brent crude, used to price international oils, rose 10 cents to $66.91 per barrel in London. It gained 6 cents the previous session to $66.81.
CURRENCY: The dollar gained to 110.04 yen from Monday's 109.96 yen. The euro advanced to $1.1317 from $1.1313.