* Euro zone service sector PMI eases recession fears
* Euro rises to near 3-week high vs dollar, 4-week high vs yen
* Greek debt negotiations stall but hope for deal still alive
By Nia Williams
LONDON, Jan 24 (Reuters) - The euro slipped after hitting a near three-week peak versus the dollar in choppy trade on Tuesday, as concerns over the outcome of talks to avert a messy Greek default outweighed the impact of a better-than-expected survey of the euro zone service sector.
Surveys showed the euro zone may yet escape recession thanks to a surprise upturn in the service sector which offset ongoing contraction in manufacturing this month, briefly pushing the euro to the day's highs.
The single currency rose to $1.3063 on trading platform EBS, its highest level in nearly three weeks, before falling back to $1.2997, down 0.2 percent on the day. Traders cited strong selling by a hedge fund that pressured on the euro.
Uncertainty over Greece's ability to avert a chaotic default contributed to increased market volatility after euro zone finance ministers sent back a Greek debt swap offer, saying the coupon demanded by bondholders was too high.
Private creditors have said a 4.0 percent coupon is the least they can accept if they are going to write down the nominal value of the debt they hold by a half.
"Euro zone PMIs probably helped but we are not trading the euro on growth prospects. We are more worried about the structural implications of the euro crisis and the headlines we are waiting for with regards to Greece and a PSI (private sector involvement) deal," said Carl Hammer, chief currency strategist at SEB.
The euro held well above its 17-month EBS low of $1.2624 hit on Jan. 13. Topside resistance was at $1.3077/1.3100, the Jan. 3 high and a 38.2 percent retracement of the November-January slump. Traders said a break above the October EBS low of $1.3145 was still needed to turn the technical picture positive.
IMM speculative positioning data shows an extreme short position in the euro, which leaves it vulnerable to pullbacks, but market participants were sceptical over the sustainability of any rallies.
"Sooner rather than later sellers will appear again, although there is a bit more short covering to happen before we will continue a euro downtrend," said SEB's Hammer.
The euro was pressured by suggestions that Portugal, seen as the second most risky country in the euro zone, could be the next potential default candidate after Greece.
Germany also tempered optimism by denying a report that it was ready to boost the combined firepower of the euro zone's rescue funds to 750 billion euros ($979 billion).
Despite the better PMI surveys, many market players expect the euro to endure a prolonged period of sluggish growth, forcing the European Central Bank to keep interest rates low.
Jaco Rouw, senior currency strategist at ING Investment Management, said the ECB's stance in providing long-term low-rate funding for European banks meant the euro had become the funding currency of choice.
"The euro region will be one of the weakest in the world, it will see a recession. Rate cuts will make the euro a more attractive funding currency," Rouw said.
Against the safe haven Swiss franc the euro fell to a four-month low of 1.2057 francs with traders reporting bids at 1.2050-40 francs.
BOJ ON HOLD
Against the yen, the euro hit a near four-week high of 100.84, moving further away from an 11-year EBS low of 97.04 marked on Jan. 16. Traders cited Japanese importer demand triggering stop-losses around 100.50.
The dollar rose to a near four-week high of 77.39 yen in a move which traders said was largely driven by euro/yen demand. Reaction was muted to the Bank of Japan's widely expected decision to hold policy steady at its regular meeting, as well as cut its economic forecasts.
Waning risk appetite pressured commodity currencies, with the Australian dollar slipping 0.6 percent to $1.0466, off a 12-week peak of $1.0574 set on Monday.
Investors also awaited the outcome of the Federal Reserve policy meeting that starts later on Tuesday.
While no policy change is expected, the Fed will likely show that its policymakers do not expect to start hiking interest rates again until the first half of 2014, more than five years after chopping them to near zero.