* Asian equities encouraged by upbeat US jobs report

* US, EU bonds supported by soft inflation, safe-haven bid

* Dollar steady after failing to sustain post-jobs rally

By Wayne Cole

SYDNEY, May 5 (Reuters) - Asian share markets inched ahead on Monday as a robust U.S. jobs report was taken as positive for global growth prospects even as a lack of inflation pulled down bond yields across the United States and Europe.

Market holidays in Japan and South Korea thinned trade, as did caution over the crisis in Ukraine.

Pro-Russian militants stormed a Ukrainian police station in Odessa on Sunday and freed nearly 70 fellow activists, two days after over 40 pro-Russian activists died in a blaze at a building they had occupied.

Australia's market gained 0.5 percent in early business , while MSCI's broadest index of Asia-Pacific shares outside Japan edged up 0.2 percent.

HSBC will release its final reading on China's manufacturing sector at 0145 GMT. The preliminary survey showed a downturn in factory activity eased slightly in April as declines in new orders and output slowed.

Japanese stocks could draw demand later in the week given reports the government was likely to say next month that it will lower the effective corporate tax rate to 20 percent from around 35 percent currently, according to the Yomiuri newspaper.

On Wall Street, the Dow ended Friday 0.28 percent lower, while the S&P 500 lost 0.13 percent and the Nasdaq 0.09 percent.

Still, all the indices were up for the week. The Dow and S&P both added 0.9 percent, and the Nasdaq 1.2 percent.

The soft finish on Friday was a disappointment given the strength of the U.S. payrolls report.

The increase of 288,000 in U.S. jobs was the largest since January 2012 and handily above forecasts. Unemployment dropped to 6.3 percent, though largely because of a steep fall in participation as more people left the labour force.

INFLATION ABSENT

Crucially for bonds, there were scant signs of inflationary pressure in the report with average weekly earnings unexpectedly soft, just the latest evidence of muted wages growth.

The general absence of price pressures has helped longer-dated Treasuries rally hard in recent weeks with yields on 30-year paper diving to 10-month lows on Friday.

That in turn has sharply narrowed the gap between short- and long-term yields, a flattening of the curve that points to a marked lessening in inflation fears.

All of which is one reason investors still assume the Federal Reserve will be in no hurry to raise interest rates. The futures market generally has a first move pencilled in for the middle of next year and a slow-paced tightening thereafter.

"For the Fed, the recent data is strong enough to validate the status quo - ongoing $10bn per meeting tapering and the first rate hike in Q2 or Q3 next year," said analysts at Commonwealth Bank of Australia.

"But pointing in the other direction is the general patchiness of data in recent months, ongoing tensions in the Ukraine, excessive short positioning and perhaps a loss of bullish sentiment in U.S. equities."

The fall in U.S. yields has also undermined support for the dollar, which notably failed to sustain a post-jobs rally on Friday.

Early Monday, the euro was steady at $1.3871 having recovered from a low of $1.3812 on Friday. Against the yen, the dollar was back at 102.23, having retreated from a near one-month peak of 103.03.

The dollar index had initially rallied to a high of 79.852 on Friday, only to then slide to a session low of 79.469. It was last flat at 79.506.

Among commodities, oil prices were mixed in slow trade. U.S. crude futures gained 1 cent to $99.77 a barrel while Brent crude eased 6 cents to $108.53.

Gold held firm at $1,300.19 an ounce after bouncing over $14 on Friday.

(Editing by Shri Navaratnam)