Global stock markets have retaken some ground after Monday's worldwide slump triggered by fears over oil prices and looming US interest rate rises.
Stock markets worldwide have seen modest rises
In New York, the Dow Jones industrial average closed up 0.3% at 10,019.47 points, scraping back above 10,000, and the Nasdaq rose 1.8% to 1931.35.
The UK's FTSE 100 index gained 1.3%, Frankfurt's Dax 30 added 1.7% and Paris's Cac 40 rose 1.4%.
But oil prices rose again, as US light crude closed above $40 a barrel.
Bargain hunting drove the gains on Tuesday, but analysts said that further falls in stock prices were likely.
"People are still leery of the market because of looming inflation and higher interest rates," said Jay Suskind, director of trading at Ryan, Beck & Co.
"Right now, you're seeing the markets pause a bit. I
think we're re-evaluating the sell off to see if it's been
an overreaction," said Stephen Sachs of US-based Rydex Investments, adding "We definitely have room to go down more".
But Tim Heekin, director of trading at San Francisco investment bank
Thomas Weisel Partners, said dealers were trying to look at "the positives".
"Corporate earnings are good, corporate
America is improving, corporate America is hiring and corporate America is increasing capital spending," he told Reuters news agency.
Tokyo's Nikkei had ended the day up 0.2%, after big losses on Monday saw it fall almost 5% and the European markets drop more than 2%.
A more robust economy
The jitters which hit on Monday were partly the result of economic strength, not weakness.
Solid numbers from the US, such as unexpectedly strong job growth, are seen as upping the odds that the Federal Reserve will raise US rates this year from their half-century low of 1%.
And China's booming economy is being tipped as a possible candidate for rate gains to take the edge off too-rapid growth.
But with tension continuing to ratchet up in the Middle East and oil prices which have recently topped $40 a barrel - although Saudi Arabia is mooting an output increase - there is plenty of downside on the agenda as well.
In any case, many say that the run-up in global markets over the past 18 months meant shares were due for a correction.
Concerns about the huge deficits in the US spell worries about the medium-term health of the US economy, said Justin Urquart-Stewart of 7 Investment Management.
"Beware, there's going to be more of this," he told BBC News.
Analysts maintained that Japanese shares had dropped too far, in light of the country's rebounding economy and improving corporate
"There wasn't any particular reason to sell Japanese stocks apart from the US rate hike jitters," said Terushi Hirotama, head of trading at Ichiyoshi Securities.
"Even so, stocks have been sold too much," he added.