* Euro's gains capped as concerns about Greece remain
* Euro zone won't authorize more money for Greece on Monday
* China data shows economy recovering
* U.S. fiscal worries hit appetite for risky assets
By Julie Haviv
NEW YORK, Nov 12 (Reuters) - The euro rose for the first time in four sessions against the dollar on Monday after recently hitting a two-month low as Greece's approval of a tough 2013 budget and upbeat Chinese economic data caused risk aversion to recede somewhat.
The single currency, however, is down about 1.9 percent against the dollar so far in November, and further gains are seen as limited given uncertainty about Greece's ability to repay its debt and a bleak economic backdrop in the region.
The euro zone will not authorize more money for Greece on Monday, despite the country approving a tough 2013 budget, because there is still no agreement on how to make its debts sustainable.
"The key question is if the latest tranche of aid will be released in time for Greece to meet a November 16th deadline on five billion euros in debt payments," said Omer Esiner, chief market analyst at Commonwealth Foreign Exchange in Washington.
"While a deal later this week would likely support the euro, its overall gains should continue to be capped by mounting worries about economic malaise spreading from the bloc's periphery into its core," he said.
The euro last traded up 0.1 percent at $1.2718, off a two-month low of $1.2688 struck on Friday, according to Reuters data. Traders cited stop loss sell orders below $1.2685 with option expiries at $1.2700 and $1.2750.
This was likely to keep the euro between $1.2690 and $1.2750.
Trade in the U.S. was on the light side, with the government bond market closed in observance of the U.S. Veterans Day holiday.
While the passage of the budget removed some of the near-term uncertainty surrounding Greece, the euro is likely to remain under pressure until an agreement on how to make Greek's debt more sustainable is reached.
"What we are seeing in the past month has been a gradual erosion of investor confidence in the euro zone and that is starting to lead to renewed downward pressure on the euro," said Lee Hardman, currency economist at Bank of Tokyo-Mitsubishi UFJ in London.
"Ultimately the situation of Greece remains unsustainable and these really are measures to kick the can down the road rather than actually dealing with the situation effectively."
Chinese data suggesting it is recovering from slower growth assuaged concerns about the world's second-largest economy.
Looking ahead, however, the euro will be swayed by data due later this week, which is forecast to show a slowdown in German growth in coming quarters and France slipping into recession.
U.S. FISCAL WORRIES
Concerns about the so-called U.S. fiscal cliff has seen safe-haven flows into the dollar and kept it near a two-month high against a basket of currencies.
Demand for riskier currencies has been sluggish as investors fret about the possible impact of some $600 billion in expiring tax cuts and spending reductions due to take effect in January.
The dollar bought 79.38 yen, down 0.1 percent from Friday's close but up from that day's low of 79.06 yen, its weakest in nearly three weeks, according to Reuters data.
Markets shrugged off a 0.9 percent July-September quarter-on-quarter contraction in Japanese economic output, in line with forecasts. This was the first negative reading in three quarters but it added to fears that slowing global growth is pushing the economy into recession.
Morgan Stanley held to its medium-term view that the yen would weaken and said it expected dollar/yen to resume its uptrend.