Asian shares edged higher on Monday, looking to extend their recent rally to a third week should U.S. jobs figures show the expected revival in hiring in May and keep the global recovery on track.

MSCI's broadest index of Asia-Pacific shares outside Japan (.MIAPJ0000PUS) was a fraction firmer, having rallied 2.2% last week. Japan's Nikkei (.N225) was flat, while Australia (.AXJO) rose 0.2% to a fresh all-time peak.

Markets in the U.S. and UK are closed for a holiday, but futures were still trading in Asia with the Nasdaq up 0.2% and S&P 500 ahead by 0.1%.

The main event of the week will be U.S. payrolls on Friday with median forecasts at 650,000 but the outcome uncertain following April's shockingly weak 266,000 gain.

That April figure was close to 750,000 lower than forecasts, the largest "miss" in the history of the series.

NatWest Market economist Kevin Cummins noted that even with a rise of around 550,000 total payrolls would still be 7.7 million below the February 2020 level.

"The labour market would still be considered a long way from being recovered," he added. "In our opinion, the data are unlikely to convince Fed Chair Powell that progress has been substantial enough just yet to start signalling tapering."

The Federal Reserve next meets on June 16 and this week will be the last chance for members to talk on policy before the blackout period starts on June 5.

So far, investors have taken the Fed at its word that the labour market needs to improve a lot more before it talks of tapering. That helped yields on U.S. 10-year notes ease to 1.58% on Friday even as data on core inflation topped forecasts.

The economic outperformance of the United States has a downside in that it has sharply widened the country's trade deficit and added to its need for foreign funding for an already huge budget shortfall.

"The U.S. economy will face a period of high fiscal deficits and rising debt levels for the foreseeable future, ensuring that 'twin deficit' risk for the USD will remain a feature of the market landscape for years to come," said Ray Attrill, head of FX strategy at NAB.

The dollar index stood at 90.062 , near a five-month low . The euro was steady at $1.2190 , just off a four-month high of $1.2266 hit last week.

The dollar has fared better on the Japanese yen as investors borrow the currency at super-low rates to buy higher-yielding assets. The dollar was last at 109.93 yen after touching a two-month top of 110.19 last week.

China's yuan has gained 1.7% so far in May to trade at three-year highs and breach the psychologically important 6.4 per dollar level.

Concerns about global inflation and extreme volatility in cryptocurrencies has been a boon for gold which was holding at $1,903 , after hitting a four-month high at $1,1912 last week.

Oil prices were firm after gaining more than 5% last week to reach two-year closing highs as expectations of a rebound in global demand outweighed concerns about more supply from Iran once sanctions are lifted.

All eyes will be OPEC this week as it reviews its supply agreement, and any hint of an increase in output could pressure prices.

Brent added 21 cents to $68.93 a barrel, while U.S. crude rose 26 cents to $66.58.