But investors remain wary of any further upheaval in the US financial system following last week's turmoil that saw the sale of the embattled First Republic Bank to JPMorgan Chase.
That followed the collapse in March of three other banks and the takeover of Credit Suisse by UBS, which sparked panic on trading floors.
An indication last week from the US Federal Reserve that it could pause its interest rate hikes -- after announcing another increase -- did little to soothe concerns.
Still, a surge Friday in US regional lenders and the strong jobs report provided a shot in the arm for Asian markets at the start of the week.
Hong Kong, Shanghai, Mumbai and Bangkok led gainers by putting on more than one percent each, while Sydney, Seoul, Taipei, Wellington and Jakarta were also in the green.
But Tokyo was dragged down by a retreat in banks as investors returned from an extended break to play catch-up with last week's sell-off.
Paris and Frankfurt were slightly higher in the morning. London was closed for a holiday.
- Jobs data jump -
While the quarter-of-a-million jump in the non-farm payroll figure will give the Fed reason to hold rates higher for longer, it also showed the US economy remained resilient despite higher rates and inflation.
Investors have fretted for months that the long-running programme of monetary tightening aimed at defeating soaring prices will spark a recession.
Chicago Fed chief Austan Goolsbee warned on Friday it was "way too premature" to say if there would be another lift next month but warned the banking turmoil would likely drag on the economy.
There were growing worries about a possible catastrophic US default, with Treasury Secretary Janet Yellen warning the country could run out of cash to pay its bills as soon as the start of June unless Congress raises the debt limit.
While many commentators believe lawmakers will come to a deal to lift the borrowing ceiling, as they have every time in the past, there remain fears that the unthinkable could happen and spark an economic crisis.
"Anxiety over US default is at an all-time high," said SPI Asset Management's Stephen Innes.
"Historically, markets have not started worrying about a debt limit default until 2-4 weeks before the anticipated x-date (believed to be the end of July).
"But anxiety is building early this time and shifted into high gear last week after Secretary Yellen warned that a default could occur as soon as June 1."
- Key figures around 0810 GMT -
Tokyo - Nikkei 225: DOWN 0.7 percent at 28,949.88 (close)
Hong Kong - Hang Seng Index: UP 1.2 percent at 20,297.03 (close)
Shanghai - Composite: UP 1.8 percent at 3,395.00 (close)
Euro/dollar: UP at $1.1052 from $1.1022 on Friday
Pound/dollar: UP at $1.2644 from $1.2632
Dollar/yen: UP at 134.98 yen from 134.83 yen
Euro/pound: UP at 87.41 pence from 87.22 pence
West Texas Intermediate: UP 1.0 percent at $72.34 per barrel
Brent North Sea crude: UP 1.0 percent at $76.26 per barrel
New York - Dow: UP 1.7 percent at 33,674.38 (close)
London - FTSE 100: Closed for a holiday
dan/dva
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