Stock and bond markets attempted to steady on Tuesday, as investors turned their focus to this week's U.S. labour market report, to gauge if interest rate hikes that have been priced in around the world are justified.

By mid-morning, MSCI's broadest index of Asia-Pacific shares outside Japan was down 0.4%, while Japan's Nikkei stock index rose nearly 1%, in part helped by a fresh round of weakness in the Japanese yen.

Wall Street indexes fell on Monday, but the pace of selling was reduced and U.S. stock futures were steady in Asia.

Besides interest rates, the health of China's economy is also at the forefront of investor concerns. China's benchmark Shanghai Composite Index lost 0.4% in early trade.

Hong Kong's Hang Seng index fell 1.8% as investors start to walk back their enthusiasm about an agreement struck between China and the United States for access to Chinese companies audit papers.

At the Jackson Hole conference last week, Federal Reserve Chair Jerome Powell and European Central Bank speakers struck a hawkish tone, driving selling of bonds and equities as traders jacked up near-term interest rate expectations.

"The markets focus for the next couple of weeks at least, will be the likely Fed action," said Manishi Raychaudhuri, head of APAC equity research at BNP Paribas.

"Earlier, there was talk of a pivot of a possible cutting of interest rates by the Fed, maybe in 2023 second half or so, but that is now sort of falling by the wayside," he said.

"Higher for longer (interest rate) is possibly the kind of narrative that's building up," he said.

Futures markets have odds of better than two-thirds that the ECB raises rates by 75 basis points in September, and see about a 70% chance that the Fed does likewise.

U.S. non-farm payrolls data is due on Friday, and markets may not like a strong number if it supports the basis for a continuation of aggressive interest rate hikes.

U.S. Treasuries settled down on Tuesday morning. The two-year yield fell to 3.4293%, after rising as high as 3.489% on Monday, its highest since late 2007.

Benchmark 10-year yields also fell to 3.0949%, down from 3.13% on Monday.

The U.S. dollar steadied after an overnight dip, though the euro was already struggling to hang on to small gains driven by ECB hike bets and a cooling of gas prices. [FRX/]

The dollar index, which measures the currency's value against a basket of peers, rose 0.2% to 108.85, not far from the two decade peak of 109.48 it made a day earlier. The dollar traded at $0.9987 per euro and bought 138.59 yen.

Oil mostly held gains on the prospect of output cuts, as traders look ahead to a producers meeting on Sept. 5. U.S. crude was about 30 cents a barrel weaker at $96.68 and Brent crude fell 68 cents to $104.41.

Gold was slightly lower. Spot gold was traded at $1,735.95 per ounce.

(Editing by Jacqueline Wong)