Bargain buying saw Seoul's Kospi lead gains and reclaim most of the 8.3 percent lost in Monday's plunge that was sparked by bets on a US interest rate hike and fears over tech firms' valuations.
News that the US economy had created more than double the number of jobs than expected in May indicated it remained in rude health but put pressure on the Federal Reserve to tighten monetary policy as it also battled surging inflation.
That came after disappointing revenue forecasts from chip giant Broadcom sparked jitters about the AI sector, which has helped drive markets to record highs this year.
A plunge in tech firms in New York on Friday was followed by a similar collapse for their Asian counterparts on Monday, sending Seoul's Kospi down more than eight percent.
However, analysts said the selling was largely driven by profit-taking and could be seen as a healthy pause in a rally that has run since March.
The strong showing in Asia followed a rebound on Wall Street, where the Nasdaq and S&P 500 advanced.
Following the Kospi's lead, Taipei added 2.8 percent and Tokyo more than two percent.
Hong Kong, Shanghai, Singapore, Manila, Mumbai, Bangkok and Wellington were also up, although Sydney edged down.
Jakarta rallied more than four percent as the Indonesian rupiah climbed against the dollar after the central bank in Jakarta announced a surprise 25-basis-point interest rate hike.
- 'By no means the end' -
There was little major reaction to data showing Chinese exports and imports soared last month.
"Expectations of tighter monetary policy, combined with underwhelming results from Broadcom last week, raised questions over the pace of the sector's rally and prompted investors to take profits," wrote Fiona Cincotta at City Index.
"This is by no means the end of the AI trade, but it does suggest that valuations had become stretched in parts of the market."
Investors also took heart from news that Iran and Israel said on Monday they had halted hostilities after exchanging strikes that threatened to reignite the Middle East war.
Israeli Prime Minister Benjamin Netanyahu announced that the "fire on that front is contained" hours after Tehran said it had stopped its military action.
Iran launched missiles at Israel on Sunday over its ongoing war against Hezbollah in Lebanon. Israel then struck back, despite efforts by US President Donald Trump to dissuade Netanyahu.
That triggered another round of Iranian missiles, before Tehran announced it would cease fire.
Fears had grown that the flare-up would put at risk a fragile Middle East truce -- in place since April 8 -- and ruin efforts for peace talks to reopen the Strait of Hormuz, through which about a fifth of global crude usually passes.
Trump added to the optimism on Tuesday by saying negotiators were in the "final throes" of talks for a peace deal.
Oil prices, which had spiked more than five percent earlier Monday, pared earlier gains and were down on Tuesday.
Eyes are now turning to the release on Wednesday of US inflation, which could play a key role in the Fed's rate decision-making. The consumer price index is expected to hit 4.2 percent, a more than three-year high.
Stock markets in London, Paris and Frankfurt opened lower.
- Key figures at around 0715 GMT -
Seoul - Kospi: UP 8.2 percent at 8,096.93 (close)
Tokyo - Nikkei 225: UP 2.2 percent at 65,416.63 (close)
Hong Kong - Hang Seng Index: UP 0.2 percent at 24,695.58
Shanghai - Composite: UP 1.3 percent at 4,010.03 (close)
London - FTSE 100: DOWN 0.4 percent at 10,328.76
West Texas Intermediate: DOWN 1.4 percent at $90.07 a barrel
Brent North Sea Crude: DOWN 1.1 percent at $93.98 a barrel
Euro/dollar: UP at $1.1543 from $1.1531 on Monday
Pound/dollar: UP at $1.3361 from $1.3341
Dollar/yen: DOWN at 160.16 yen from 160.21 yen
Euro/pound: DOWN at 86.39 pence from 86.44 pence
New York - DOW: DOWN 0.2 percent at 50,786.01 (close)
dan/pbt