The euro rose slightly against the dollar on Tuesday but lingering concerns over the euro zone's debt crisis limited its gains, while Asian tech shares rallied on hopes for a recovery in battered memory chip prices.

News that Apple Inc CEO Steve Jobs is taking medical leave for the third time since 2004 also prompted the view that its Asian rivals may slow the runaway success of the iPhone and iPad maker. But investors wanted to see Wall Street's reaction later in the day.

Hopes for improvement in the euro zone debt crisis after relatively smooth bond auctions in Portugal and Spain were being tested by Germany, which saw no urgency to beef up the currency bloc's bailout fund.

What indications we have heard from European officials over the past several days is that they just don't feel the same sense of urgency that the market does, said Todd Elmer, currency strategist with Citi in Singapore.

I think for the time being that means the euro is likely to trade lower, Elmer said, adding that the euro could dip back toward $1.30 in coming weeks.

Speaking after a monthly meeting of the euro zone finance ministers on Monday, the group's chairman, Jean-Claude Juncker, was careful not to commit to being ready for a new package of measure to end the debt crisis in time for the February 4 or March 24-25 European Union leaders' summits.

The euro inched higher to $1.3312 as of 11:01 a.m. EST, after having slid to a low of around $1.3243 overnight, well off a one-month high near $1.3460 set last Friday.

Europe set up the safety net fund, which can borrow on the markets with euro zone government guarantees of up to 440 billion euros, in response the debt crisis that forced Greece and Ireland to take bailouts last year.

As worries over the euro zone's debt crisis linger, Greece's deputy prime minister said on Monday extending the repayment of the nation's debt could help the overborrowed country emerge from its debt crisis.

Some traders said signs of stability in China's stock market <.SSEC>, after a 3 percent slide on Monday, may also have helped underpin the euro.

APPLE'S IMPACT EYED

Stock market players awaited Wall Street's reaction to Apple's announcement, which knocked U.S. stock futures sharply lower on Monday when U.S. markets were closed for a public holiday.

Apple's market capitalization is about as big as Japan's 11 biggest tech firms combined. The impact of its news could be mixed for Asian technology rivals.

Some could benefit if Apple's success slows, boosting the popularity of their own products, but others in the supply chain rely on its orders for displays, chips, phone cases and other accessories associated with its popular gadgets.

Japan's Nikkei average <.N225> closed up 0.15 percent, while the MSCI index of Asia and Pacific shares excluding Japan <.MIAPJ0000PUS> rose 0.5 percent.

Tech shares outperformed, however, with the MSCI Asian IT index outside of Japan <.MIASJIT00PUS> up 1.3 percent.

Shares of Samsung Electronics Co <005930.KS>, a rival to Apple in some business areas and the world's top memory chipmaker, jumped as much as 3.3 percent to record highs after a newspaper report that Japan's Elpida planned to raise chip prices by about 10 percent.

Elpida <6665.T> ended 1.1 percent higher on the report.

The Shanghai Composite Index <.SSEC> fell 0.2 percent after slumping a day earlier in reaction to China's decision on Friday to raise lenders' reserve requirements. The decline weighed on bourses across Asia which have drawn considerable support from China's robust economic growth.

But Hong Kong's Hang Seng Index <.HSI> managed to avoid the downdraft and rose 0.6 percent on hopes for stronger corporate earnings.

U.S. crude futures were little changed above $91 a barrel on Tuesday after falling the previous day when the dollar strengthened and a major Alaskan oil pipeline resumed full operations.

(Additional reporting by Ian Chua in Sydney, Antoni Slodkowski in Tokyo, and Miyoung Kim in Seoul, and Masayuki Kitano in Singapore)

(Editing by Kim Coghill)