MSCI's broadest index of Asia-Pacific shares outside Japan was down 0.1 percent, after US stocks ended the previous session with mild gains. The index is up 1.6 percent so far this month.

Australian shares were down 0.21 percent, while Japan's Nikkei stock index slid 0.77 percent.

Hong Kong's Hang Seng Index was flat in early trade and China's CSI300 Index off 0.16 percent.

The yield on benchmark 10-year Treasury notes reached 4.4001 percent compared with its US close of 4.402 percent on Monday. The two-year yield, which rises with traders' expectations of higher Fed fund rates, touched 4.8184 percent compared with a US close of 4.818 percent.

On Monday, US Treasury yields fell to the lowest point in two weeks, after the country's manufacturing activity slipped for the second consecutive month in May.

The 2-year yield was 6 basis points lower while the 10-year yield was down 11 basis points.

"The sharper move at the long-end is a sign that weaker manufacturing data is unlikely to shift the dial on Fed rate cuts near term, but is perhaps a signal of the market's view of neutral interest rates as US economic exceptionalism fades," Westpac economist Jameson Coombs said in a note on Tuesday.

There was now 40 basis points of rate cuts by the end of 2024 priced into financial markets expectations, he added.

In Europe, investors expect the European Central Bank on Thursday to cut the benchmark rate by 25 basis points to 3.75 percent.

On Wall Street, the S&P 500 index edged up 0.1 percent, the Dow Jones Industrial Average shed 0.3 percent, and the Nasdaq Composite rose 0.6 percent.

In India, Prime Minister Narendra Modi is expected to win a record-equalling third consecutive term in office on Tuesday when the 642 million votes cast in the world's largest election are counted.

The outcome is expected to be positive for the country's financial markets, according to analysts, on the hope India will undergo further economic reform.

The dollar rose 0.16 percent against the yen to 156.35 in Asian trading on Tuesday. It is still some distance from its high this year of 160.03 in late April.

The European single currency was up 0.1 percent on the day at $1.0912, having gained 0.65 percent in a month, while the dollar index, which tracks the greenback against a basket of currencies of other major trading partners, was down at 104.

US crude dipped 0.42 percent to $73.91 a barrel. Brent crude fell to $78.05 per barrel. Both benchmarks slid to four-month lows on Monday after the Organization of the Petroleum Exporting Countries and allies, together known as OPEC+, agreed to start unwinding some production cuts from October.

"Most commodity analysts had expected the production cuts to be maintained till the end of the year," NAB economists said.

Gold was slightly higher. Spot gold was traded at $2350.73 per ounce.