Share markets were mixed following a soft finish on Wall Street though sentiment was supported by speculation the Federal Reserve would be patient in tightening policy given the weakness of wages apparent in the jobs numbers.
Wages fell by the most since the series began in 2006 even as payrolls increased by a brisk 252,000.
Treasury yields fell sharply on the news as the market pushed out the likely timing of the first rate hike, which in turn undercut the dollar.
The greenback dipped as far as 118.12 yen first thing on Monday, reaching a low last seen on Jan. 6, before steadying at 118.30.
The euro edged up to $1.1865 and away from last week's nine-year trough of $1.1754.
The dollar index slipped to 91.788, off a nine-year peak of 92.528 scaled last week.
With Tokyo shut, there was little initial reaction to news Japan's government planned a record budget for next fiscal year of more than $800 billion as Prime Minister Shinzo Abe seeks to shore up the economy.
Australia's share market started the new week with a loss of 0.5 percent, but MSCI's broadest index of Asia-Pacific shares outside Japan gained 0.2 percent.
On Wall Street, the Dow ended Friday down 0.95 percent, while the S&P 500 fell 0.84 percent and the Nasdaq 0.68 percent.
The US corporate earnings season starts this week and expectations are low given sluggish global growth and the strength of the dollar.
Euro zone share markets had been pressured in part by reports the European Central Bank had still not decided on a plan for quantitative easing and might buy only 500 billion euros of government bonds.
Investors have been wagering that the purchases would be at least twice that and would be announced in full at the next policy meeting on Jan. 22.
Italy's central bank chief warned on Sunday the risk of deflation in the euro zone should not be underestimated.
He said the best way to deal with the problem was to buy government bonds.
In commodity markets, oil prices remained under pressure having hit their lowest since April 2009. Brent was quoted down 92 cents at $49.19 a barrel, after touching a trough of $48.90 on Friday.
US crude skidded 83 cents to $47.53 a barrel. The drop in the dollar helped gold nudge up to its highest in a month around $1.226.80 an ounce.