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* Asian stock markets: https://tmsnrt.rs/2zpUAr4
* Major Wall St indexes at record highs on rising rate cut hopes
* Global bond rally continues; Treasury yield hits 32 month-low
* Trade subdued, U.S. financial markets closed for holiday
TOKYO, July 4 (Reuters) - Asian stocks advanced on Thursday, tracking sharp gains on Wall Street as recent data from multiple sectors pointed to slowing economic growth in the United States, bolstering the prospect of rate cuts by the Federal Reserve.
MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.3% as did Japan's benchmark Nikkei , and Australia was up 0.6%. A U.S. public holiday kept activity somewhat subdued.
On Wall Street, which closed at midday Wednesday for the eve of the U.S. Independence Day, all three major stock indexes finished at a record closing highs as expectations grew that the Fed would take a more dovish turn.
A report by a payrolls processor ADP showed U.S. companies added jobs in June, but fewer than what analysts had forecast, raising concerns the labour market is softening even as the current U.S. economic expansion marked a record run last month,
"Stocks and bonds rallied together overnight as the markets were betting on interest rate cuts at the European Central Bank and the U.S. Federal Reserve," said Noriko Miyoshi, head of fixed income at Simplex Asset Management in Tokyo.
"The pace looks too fast. Investors across the world rushed to take part in the game of yield hunting," she said.
Global sovereign bond rallied overnight. The 10-year Treasury note yield plunged to 1.939, a level last seen following Donald Trump's election as president in November 2016.
Most 10-year euro zone bond yields,, , slid to fresh record lows on Wednesday as investors bet the ECB's dovish stance would continue, while the 10-year German Bund yield fell to minus 0.399%, flirting with the ECB's minus 0.40 deposit rate.
European Union leaders' nomination of Christine Lagarde, the head of the International Monetary Fund, to replace Mario Draghi as president of the ECB, reinforced expectations of more monetary policy easing if it's needed.
The 10-year Italian bond yield hitting 1.599%, its lowest since October 2016 as the government eases its budget ambitions.
The market's next focus is U.S. non-farm payrolls for June, due on Friday.
In the foreign exchange market, the euro traded at $1.1288 , near its two-week low of $1.1268 set the previous day.
The dollar was little changed at 107.72 yen, losing steam as the fall this week in U.S. bond yields.
The British pound stood at 1.2580, having hit a two-week low of $1.2557 as economic data reinforced expectations that the Bank of England would join its central bank counterparts in cutting interest rates to shore up a worsening economic outlook.
In commodities, oil prices slipped on Thursday after edging higher the previous day.
Brent crude futures traded down 0.4% at $63.58 per barrel in early Asian trade on Thursday, while U.S. crude futures fetched $57.15 per barrel, down 0.3 percent. (Reporting by Tomo Uetake; Editing by Richard Borsuk)