* Euro rebounds strongly against the dollar
* Greece uncertainty continues to weigh on some investors
* Dollar rises vs yen after NY factory data, TICs data (Recasts, updates prices)
NEW YORK, Feb 16 (Reuters) - The euro rebounded against the dollar to post its biggest one-day gain since July on Tuesday, as traders bet the single currency had slipped too far in recent weeks over worries about Greece's public finances.
A rise in U.S. stocks illustrated rising risk appetite among investors.
Investors were still cautious, however, amid uncertainty over whether Greece's debt problems will be resolved quickly.
"A brief pause in European-related headlines perhaps offers hope for a corrective bounce (in the euro) in the coming days," said Nick Bennenbroek, head of currency strategy at Wells Fargo Bank in New York.
Analysts said the euro remained highly sensitive to any more negative news on Greece.
"The main focus is still on Greece and the debt problems on the periphery of the euro zone," said Jacob Oubina, senior currency strategist at FOREX.com, in Bedminster, New Jersey.
Euro zone states urged Greece on Monday to take further steps to control its budget deficit by mid-March if needed, but did not elaborate on last week's pledge by the European Union to help Greece. [
]In mid-afternoon trading in New York, the euro <EUR=> was up 1.2 percent on the day at $1.3764, after touching a session high at $1.3775 earlier, which marked the biggest one-day gain since July.
In the United States, a gauge of manufacturing in New York State jumped in February to its highest level since October, and another report showed net overall capital inflows increased to $60.9 billion in December. [
] [ ]That data helped the dollar against the yen, though some analysts said the greenback rise was more on yen weakness than dollar strength. The dollar rose 0.2 percent against the yen to 90.17 <JPY=>, while the euro <EURJPY=> gained 1.4 percent to 124.12 yen.
Against the Swiss franc, the dollar fell 1.1 percent to 1.0659 francs <CHF=>, which was the biggest one-day fall since Nov. 25.
FURTHER LOSSES?
The euro is still down 3.8 percent against the dollar in 2010 to date on worries over the fiscal health of Greece and other euro zone countries, such as Portugal.
"Should the euro fail to gain any traction, it would be a signal of further losses to come for the single currency." said Bennenbroek at Wells Fargo.
Traders said the euro was also boosted against the U.S. dollar in tandem with the Australian dollar and other perceived riskier currencies, after Australia's central bank signaled further gradual interest rate rises. [
]But the Australian currency outshone the euro, hitting a decade high of A$1.5188 <EURAUD=R>, according to Reuters data in New York, while it also hit its strongest versus the dollar since Jan. 28 at $0.9024 <AUD=>. (Reporting by Nick Olivari amd Vivianne Rodrigues; Editing by Leslie Adler)