Tokyo, which suffered a record loss Monday, led the gains, soaring more than 10 percent as traders bought beaten-down stocks caught up in a catastrophic day for markets.
But analysts warned there would likely be more volatility to come.
The sell-off followed data Friday which showed fewer US jobs than expected were created last month, while another report pointed to continuing weakness in the manufacturing sector.
That led to warnings the Fed had kept rates at more than two-decade highs for too long and risked causing a recession.
Some analysts pointed to the "Sahm Rule," which says an economy is in the early stages of recession if the three-month moving average of unemployment is 0.5 percentage points above its low over the previous 12 months. That was triggered by Friday's data.
Commentators also said a stronger yen had led investors to unwind their "carry trades", in which they borrowed in the cheap Japanese currency to invest in higher-yielding assets, such as equities.
While Wall Street's three main indexes suffered another day of pain -- with the Nasdaq down more than three percent -- a forecast-beating read on the key US services sector provided some solace.
Tokyo's Nikkei, which tanked more than 12 percent Monday and suffered a record points loss, jumped 10.2 percent.
Toyota was up more than 12 percent, Sony piled on more than nine percent and chip giant Tokyo Electron added 16.6 percent.
"This is a sweeping, across-the-board gain," said analysts at Nomura, adding that investors would also pay close attention to the forex market.
Japan's Prime Minister Fumio Kishida said at a scheduled news conference Tuesday: "The stock market has been moving again today, and I think it is important to judge this situation calmly."
"We will continue to monitor the situation with a sense of urgency and to carry out economic and fiscal management in close cooperation with the Bank of Japan."
Shanghai, Sydney, Seoul, Taipei, Mumbai and Bangkok also rose but Hong Kong gave up early gains to finish in the red.
Singapore and Wellington also suffered more selling, while Manila was flat.
London edged up after shedding around two percent Monday, while Paris and Frankfurt were also higher.
- Yen in retreat -
Friday's data sparked calls for the Fed to cut rates now. Nobel prize-winning US economist Paul Krugman wrote on social media: "I wasn't calling for an inter-meeting cut, because that might signal panic.
"But since we may be seeing a panic anyway, that argument loses its force. Real case for an emergency cut soon."
But Chicago Fed boss Austan Goolsbee urged caution about reading too much into one jobs report.
"As you see jobs numbers come in weaker than expected but not looking yet like recession, I do think you want to be forward-looking of where the economy is headed," he told CNBC ahead of the US trading day Monday.
"The payroll jobs number is plus or minus 100,000 a month, so be a little careful over-concluding about things in the margin of error," he said, adding that if the US economy deteriorated, the Fed would "fix it".
Pantheon Macroeconomics wrote in a note to clients that the Fed "probably will place little weight on the drop in stock prices, as the main indexes still are higher than at the start of the year".
Fed chief Jerome Powell said after the bank's policy meeting last week that a cut could come as soon as September.
Bets had been for at least one 25-basis-point reduction before January but talk is now about a possible 100-basis-points-worth of cuts.
The yen's rally ran out of puff and was sitting just below 145 per dollar, having hit a six-month high below 142 Monday.
The Japanese unit has surged over the past month -- after hitting a nearly four-decade low in early July -- after the Bank of Japan hiked rates hours before Powell indicated the Fed was planning a cut.
Moody's Analytics analysts wrote: "Asia's equity selloff will cause sleepless nights at the Bank of Japan. For the past two years, the central bank had been playing it safe, wary of repeating the mistake of tightening policy right into a downturn.
"The last significant rate hikes by the BoJ were in 2006, just before the collapse of Lehman Brothers, and in 2000, just as the dot.com bubble burst. Both times, the BoJ was forced to reverse course.
"The BoJ can hardly be blamed for this latest market selloff, so another U-turn is not a foregone conclusion. But the selloff doesn't make last week's rate hike -- which was already on shaky ground -- look any better."
- Key figures around 0810 GMT -
Tokyo - Nikkei 225: UP 10.2 percent at 34,675.46 (close)
Hong Kong - Hang Seng Index: DOWN 0.3 percent at 16,647.34 (close)
Shanghai - Composite: UP 0.2 percent at 2,867.28 (close)
London - FTSE 100: UP 0.4 percent at 8,042.79
Dollar/yen: UP at 145.45 yen from 144.05 yen on Monday
Euro/dollar: DOWN at $1.0928 from $1.0959
Pound/dollar: DOWN at $1.2744 from $1.2773
Euro/pound: DOWN at 85.75 pence from 85.77 pence
West Texas Intermediate: UP 0.4 percent at $73.23 per barrel
Brent North Sea Crude: UP 0.2 percent at $76.43 per barrel
New York - Dow: DOWN 2.6 percent at 38,703.27 (close)
dan/mtp
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