Crucially, the new head of the Federal Reserve, Janet Yellen, delivers her first testimony to the House on Tuesday and the Senate on Thursday, and markets will be hoping for reassurance that policy will stay loose for a long time to come.
Japan's Nikkei led the way with a rise of 1.3% to 14,668, and away from last week's trough at 13,995.
"In the short-term, investors are covering their short positions as risk appetite has come back," said Nobuhiko Kuramochi, a strategist at Mizuho Securities.
"But they are not yet confident about further market rises until they get assurance for US policy and growth at Yellen's testimony this week."
MSCI's broadest index of Asia-Pacific shares outside Japan inched up 0.3%, while Shanghai added 1.7%.
Japanese shares found further comfort in a softening yen with the dollar grinding up to 102.41, though it failed to clear resistance around 102.60. The dollar was a shade firmer on the euro at $1.3625, against $1.3635 late Friday.
Both stocks and the dollar had initially retreated when the US payrolls report showed a rise of only 113,000 in January, well short of forecasts.
However, the damage was limited by a very strong household survey where a sharp jump in the number of people employed nudged the jobless rate down to 6.6%.
The mixed bag left Treasuries little changed with yields on 10-year notes a shade lower at 2.68%.
In commodities, oil prices initially extended their recent gains as persistently cold weather across the US continued to eat into heating fuel stocks.
US crude made an early six-week peak at $100.46 a barrel but could not force its way past the December high at $100.75. Brent crude oil futures gave up 46 cents of last week's gains to stand at $109.20 a barrel.
Spot gold was also firm at $1,268.24 an ounce, but faces stiff resistance from $1,273 to $1,278.
Fed Chair Yellen will be able to offer her own read of the jobs report before lawmakers this week.
Analysts generally assume she will stick to the script of recent policy meetings, reiterating that further gradual decline in asset buying is likely as long as the economy continues to improve as assumed.
"We expect her to state that tapering is not on a preset course and the committee will adjust course as needed, particularly if the expected firming in growth and gains in payrolls do not persist," wrote analysts at Barclays in a note.
Yellen is also likely to repeat the standard forward guidance that the funds rate will remain near zero until the unemployment rate falls well below 6.5%, so long as inflation is subdued.
Major US data includes retail sales on Thursday where a flat result is forecast due partly to bad weather and a rise in gasoline prices.
In Asia, China releases trade numbers on Wednesday and consumer prices on Friday. Analysts at Commonwealth Bank of Australia predict exports will have shrunk in January but mainly because of significant base effects as January last year saw an outsized 25% increase.
Trade flows can be very volatile in January and February because of the timing of the Lunar New Year holiday.
The euro zone releases its first estimate of economic growth on Friday and forecasts favour a slim 0.2% increase in the fourth quarter, which would keep pressure on for more action from the European Central Bank.
ECB President Mario Draghi gives a speech on "Progress Through Crisis?" on Wednesday and markets will be sensitive to any hint of further accommodation to come.
Across the Channel, the Bank of England issues its February Inflation Report on Wednesday which will likely show muted prices pressures and so support the outlook for low rates.