The closely watched non-farm payrolls reading on Friday followed a string of figures last week showing the world's top economy was slowing down and dented investor sentiment.
Focus is now on the release of inflation figures later this week, which will play a crucial role in the Fed's decision-making when it meets early next month.
While rates are seen going up, bets are for officials to end their hiking cycle earlier than previously thought, with a nervous eye on the banking sector after last month's turmoil that saw two lenders go under and Credit Suisse taken over.
Some commentators have even suggested that the Fed would announce cuts by the end of the year.
"It seems the Fed will unlikely 'budge' on cuts unless the US economy is amid a deep downturn," said SPI Asset Management's Stephen Innes.
"And given the still sticky inflation outlook and the less dovish drumbeat from the Fed speak, cuts may need to be removed from the market unless we enter an actual recession -- and of course, neither outcome is an excellent backdrop for equities."
He added that the jobs report "was encouraging, signalling a subtle rebalancing of the labour market that again points to a soft landing".
With much of the region still closed for the Easter break, trading was light again on Monday.
Tokyo, Seoul, Mumbai, Bangkok and Taipei rose but Shanghai, Singapore and Jakarta turned negative.
Expectations for another Fed hike also lifted the dollar against its peers.
Oil prices edged down as investors weighed OPEC's decision to cut output by more than a million barrels a day with the outlook for the global economy and the impact on demand.
"Economic data will form a key input this week for energy markets," said Charu Chanana, at Saxo Capital Markets.
"Given that the OPEC decision was partly intended to drive out short sellers from the crude oil market, oil prices may be better able to reflect market fundamentals."
European markets remained closed for Easter, though Wall Street reopens later in the day.
- Key figures around 0705 GMT -
Tokyo - Nikkei 225: UP 0.4 percent at 27,633.66 (close)
Shanghai - Composite: DOWN 0.4 percent at 3,315.36 (close)
Hong Kong - Hang Seng Index: Closed for a holiday
Euro/dollar: DOWN at $1.0905 from $1.0918 on Friday
Pound/dollar: DOWN at $1.2410 from $1.2443
Euro/pound: UP at 87.81 pence at 87.75 pence
Dollar/yen: UP at 132.60 yen from 131.86 yen
West Texas Intermediate: DOWN 0.2 percent at $80.56 per barrel
Brent North Sea crude: UP 0.2 percent at $84.94 per barrel
New York - Dow: Closed for a holiday
London - FTSE 100: Closed for a holiday
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