Asian shares eked out modest gains on Tuesday as buyers were held back by persistent global cost pressures, with investors turning their focus this week to U.S. inflation data and the prospects for further aggressive Federal Reserve rate hikes.

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The unexpectedly strong U.S. jobs data on Friday have raised the stakes for the July U.S. consumer prices report due on Wednesday, especially for the Fed's policy outlook.

"U.S. stocks were struggling to hold on to gains, as the focus moves from a robust U.S. labour market to the U.S. CPI data out later this week," ANZ analysts said in a note.

"The priority of reducing inflation to underpin the expansion in domestic demand and sustainable jobs growth will ring loud and clear from the 25-27 August Jackson Hole symposium."

European markets were set for a lower open with the pan-region Euro Stoxx 50 futures down 0.16 percent, German DAX futures dropping 0.16 percent and FTSE futures falling 0.12 percent. U.S. stock futures, the S&P 500 e-minis, rose 0.22 percent.

"Moves in major financial markets continue to reflect fears of a global recession. European equity futures declined. Oil prices dipped modestly in the Asia session and remain well below the highs in early June," said CBA analysts.

MSCI's broadest index of Asia-Pacific shares outside Japan was up 0.3 percent. The index is up 0.5 percent so far this month.

Japan's Nikkei slid 0.95 percent, hit by weak quarterly earnings by heavyweights and lowered expectations for the video game market, while Australian shares were up 0.06 percent.

China stocks edged up led by energy and renewable energy stocks. But the gains were capped as COVID-19 outbreaks and tensions with the United States, in the wake of U.S. House of Representative Speaker Nancy Pelosi's visit to Taiwan last week, dragged on sentiment.

China's blue-chip CSI300 index was up 0.16 percent. Hong Kong's Hang Seng index advanced 0.4 percent.

On Monday, Wall Street closed mostly flat after blockbuster jobs data last week reinforced expectations the Federal Reserve will crack down on inflation, while a revenue warning from chipmaker Nvidia reminded investors of a slowing U.S. economy.

Investors now await consumer price data on Wednesday to gauge whether the Fed might ease a bit in its inflation fight and provide a better footing for the economy to grow.

There were some encouraging signs for the Fed on the prices front, with a New York Fed survey on Monday showing consumers' inflation expectations fell sharply in July.

The Dow Jones Industrial Average rose 0.09 percent while the S&P 500 lost 0.12 percent and the Nasdaq Composite dropped 0.1 percent.

Bonds also got a safe-haven bid due to unease over Beijing's sabre rattling against Taiwan amid days of Chinese military exercises around the island.

The yield on benchmark 10-year Treasury notes rose to 2.7608 percent compared with its U.S. close of 2.763 percent on Monday. The two-year yield, which rises with traders' expectations of higher Fed fund rates, touched 3.2056 percent compared with a U.S. close of 3.216 percent.

The dollar index, which tracks the greenback against a basket of currencies of other major trading partners, was up at 106.35.

Oil prices continued their recent retreat after suffering the worst week since April on worries about stalling global demand as central banks keep tightening.

U.S. crude dipped 0.11 percent to $90.66 a barrel. Brent crude fell to $96.51 per barrel.

The rise in the dollar was a setback for gold, though it had managed to bounce from the lows hit on Friday and was traded at $1,785.67 per ounce.