* Weaker-than-expected jobs report gives Fed less reason to hike

* BOJ Kuroda underscores bank's willingness to ease further

* Oil gives back some of Friday's gains, after marking losing week

By Lisa Twaronite

TOKYO, Sept 5 (Reuters) - Asian shares rallied on Monday after last week's weaker-than-expected U.S. jobs report prompted investors to trim expectations that the Federal Reserve would hike interest rates as early as this month.

MSCI's broadest index of Asia-Pacific shares outside Japan extended early gains and was up 1.5 percent in afternoon trade.

Financial spreadbetters predicted the buoyant mood would extend into European markets, which caught a lift on Friday afternoon when the U.S. jobs report was released early in the U.S. session.

"The unemployment report was not weak enough to completely undermine the Fed's hawkish bias since Jackson Hole. It was probably enough to see fence-sitters on the Federal Open Market Committee wait until December before voting to hike interest rates," wrote analyst Jasper Lawler at CMC Markets, which expected Britain's FTSE, Germany's DAX and France's CAC to open higher.

Japan's Nikkei stock index rose 0.7 percent to its highest close since May 31. But it ended off session highs in choppy trading as the dollar slipped against the yen despite Bank of Japan Governor Haruhiko Kuroda's signal that the BOJ stands ready to ease monetary policy further.

"One positive for the market is that the correlation between the Nikkei and the yen appears to be breaking down," said Gavin Parry, managing director at Parry International Trading Ltd. "For the short-term, you have to be long Japan," he said.

U.S. stock futures edged up 0.2 percent, though cash stock and bond markets will be closed on Monday for Labor Day.

Friday's U.S. jobs report showed nonfarm payrolls rose by 151,000 jobs in August after an upwardly revised 275,000 increase in July. Economists polled by Reuters had expected a rise of 180,000.

"What matters is not whether the markets think that was a strong jobs number, but whether Fed policymakers do," said Mitsuo Imaizumi, chief currency strategist at Daiwa Securities in Tokyo, who noted that Fed Vice Chairman Stanley Fischer said late last month that the U.S. job market was close to full strength.

Richmond Federal Reserve Bank President Jeffrey Lacker said on Friday that the U.S. economy appears strong enough to warrant significantly higher interest rates.

U.S. Fed Funds futures prices indicated investors were pricing in around a 20 percent chance of a September hike, and more than a 60 percent chance by the end of year.