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* Asian stock markets :

* Markets relieved by 'goldilocks' payrolls report

* Nasdaq futures steady as G7 agrees on global corporate tax

* U.S. CPI data, ECB meeting loom large this week

SYDNEY, June 7 (Reuters) - Asian shares firmed on Monday while the dollar wavered after the anxiously awaited May U.S. payrolls report showed the recovery on track but not so hot that it might bring forward a policy tapering from the Federal Reserve.

Investors were curious to see how shares of major tech firms would react to the G7's agreement on a minimum global corporate tax rate of at least 15%, though getting the approval of the whole G20 could be a tall order.

So far, the reaction was muted with both Nasdaq and S&P 500 futures little changed.

Also of interest will be the tussle over U.S. President Joe Biden's proposed $1.7 trillion infrastructure plan with the White House rejecting the latest Republican offer.

MSCI's broadest index of Asia-Pacific shares outside Japan added 0.3% and looked to break three sessions of losses. Japan's Nikkei rose 1.0% to touch its highest in almost a month, and South Korea gained 0.7%.

While the 559,000 rise in U.S. payrolls missed forecasts it was still a major relief after April's shockingly weak report, while the jobless rate at 5.8% showed there was still a long way to go to reach the Fed's goal of full employment.

"The data was perfect for a goldilocks type outlook for risk: not too hot to bring in fears of a faster Fed taper, and not too cold to worry about the outlook for the recovery," said NatWest Markets strategist John Briggs.

"This caused a weaker USD, better stocks, reinforced the earlier bid in commodities, and boosted emerging markets."

Attention will now turn to the U.S. consumer price report on Thursday where the risk is of another high number, though the Fed still argues the spike is transitory.

Briggs suspected Fed officials might open the door to talking about tapering at the June policy meeting, with the start coming in early 2022 and a rate hike not until 2024.

The European Central Bank holds its policy meeting on Thursday and is widely expected to maintain its stimulus measures with tapering a distant prospect.

Yields on U.S. 10-year notes were a fraction higher at 1.567%, after diving 7 basis points on Friday and back to the bottom of the trading range of the last three months.

That drop, combined with an improvement in risk appetite, put the dollar on the defensive. It was last at 90.100 against a basket of currencies, having slipped from a top of 90.629 on Friday.

The euro was holding at $1.2170, after bouncing from a three-week trough of $1.2102 on Friday, while the dollar was back at 109.52 yen from a peak of 110.33.

The pullback in the dollar helped gold steady at $1,890 an ounce , up form a low of $1,855 on Friday.

Oil prices steadied after Brent topped $72 a barrel for the first time since 2019 last week as OPEC+ supply discipline and recovering demand countered concerns about a patchy global COVID-19 vaccination rollout.

Brent was up 6 cents at $71.92 a barrel, while U.S. crude added 9 cents to $69.71 per barrel.