By Stella Qiu

SYDNEY, June 5 (Reuters) -Most Asian stock markets extended a global rally on Monday on optimism the Federal Reserve would pause its rate hikes this month after a mixed U.S. jobs report, while oil jumped after Saudi Arabia pledged big output cuts.

Brent oil LCOc1 rose 1% to $76.89 a barrel, giving up some of its earlier gains to as high as $78.73, while U.S. crude CLc1 climbed 1.2% to $72.61 a barrel, after hitting a session high of $75.06.

Oil prices have recently come under pressure amid heightened concerns about China's slowing economic recovery. O/R

They rose after Saudi Arabia announced it would cut its output to 9 million barrels per day in July, from around 10 million bpd in May, the biggest reduction in years, while a broader OPEC+ deal to limit supply into 2024 also underpinned futures.

"With Saudi Arabia protecting oil prices from sliding too low ... we think oil markets are now more prone to a shortfall later this year," said Vivek Dhar, a mining and energy commodities strategist at Commonwealth Bank of Australia.

"We think Brent futures will rise to $US85/bbl by Q4 2023 even with a tepid demand recovery in China factored in."

On Monday, MSCI's broadest index of Asia-Pacific shares outside Japan .MIAPJ0000PUS gained 0.2%, while Japan's Nikkei .N225 surged 1.7% to stand above 32,000 for the first time since July 1990.

Hong Kong's Hang Seng index .HSI rose 0.6% while China's bluechips underperformed with a drop of 0.4%.

S&P 500 futures ESc1 dipped 0.1% and Nasdaq futures NQc1 dropped 0.3% in Asian hours, after a strong rally on Friday, driven by a mixed U.S. jobs report, a resolution to the debt-ceiling issue and the prospect of a U.S. rate pause this month.

Data on Friday showed U.S. economy added 339,000 jobs last month, higher than most estimates, but moderating wage growth and rising jobless rate led markets to continue to bet on no change in Fed rates this month, with a 75% chance priced in for that, according to CME FedWatch tool.

However, there is about a 70% probability that Fed funds rates would reach 5.25-5.5% or beyond at the policy meeting in July and little chance of a rate cut by the end of this year.

Treasury yields continued to climb on Monday. Yields on U.S. two-year Treasuries US2YT=RR rose 4 basis points to 4.5449%, on top of a surge of 16.2 bp on Friday, and 10-year yields also climbed 3 bps to 3.7215%, after a rise of 8 bps on Friday.

Fitch Ratings said the United States' "AAA" credit rating would remain on negative watch, despite the debt agreement.

The U.S. dollar =USD remained elevated on Monday at 104.14 against its major peers, after gaining 0.5% on Friday on the jobs report. The greenback JPY=EBS also rose 0.16% on the Japanese yen to 140.17 while the euro EUR=EBS eased 0.1% to $0.10698.

Central banks from Australia and Canada will meet this week. Markets see a sizeable chance - about 40% - that the RBA could surprise with a quarter-point hike on Tuesday, after a minimum wages decision that some economists feared could further stoke inflationary pressures.

The Bank of Canada will meet on Wednesday. A majority of economists polled by Reuters expect the BOC to keep interest rates on hold at 4.5% for the rest of the year although the risk of one more rate hike remains high.

Editing by Himani Sarkar and Sam Holmes

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