* Dollar rises as year-end factors fade
* Slower growth in U.S. services sector limits rise
* Euro weakness continues
LONDON, Jan 7 (Reuters) - The dollar rebounded against the euro and yen on Tuesday, although gains were limited by disappointing U.S. data and another fall in global stocks.
It edged up 0.1 percent to about 104.36 yen after having fallen 0.6 percent on Monday to sink as low as 103.91 yen, a low not seen since Dec. 23. It has pulled back from a five-year peak of 105.45 yen set last week.
The dollar index was up 0.1 percent at 80.739.
The move came despite Asian shares falling - to a near four-month low - which is usually a signal for safety-seeking investors to buy the yen.
The euro, which has weakened this year as factors such as banks repatriating assets before the year-end have faded, was down 0.1 percent against the dollar at $1.3619, having pulled away from Monday's one-month low of $1.3572.
After a period of low volumes over Christmas, traders are looking to events later this week for signs as to how trading in 2014 will shape up.
Foremost are the closely-watched U.S. jobs report, which may give a clue as to how quickly the Federal Reserve will taper its bond-buying, and the European Central Bank's policy meeting, as well as euro zone inflation data later on Tuesday.
Richard Falkenhall, currency strategist at SEB in Stockholm, said Tuesday's move was a continuation of the trend - which had been interrupted by year-end investor flows - for the dollar to rise as the Fed cuts back its bond-buying.
"We had some dollar weakness in the run-up to the end of last year, based on liquidity - people bought the euro and sold the dollar. To some extent that's been reversed... Over the next couple of days flows may come back into the dollar," he said.
He expects the European Central Bank to launch some form of quantitative easing around April or May and sees euro/dollar falling to $1.30-31 by the end of June and below $1.30 in the second half of the year.
"What we're seeing is a very weak euro. It's not only dollar strength," he added. "You have some divergence in monetary policy between the U.S. and the euro zone."
Two measures of activity in the U.S. services sector showed slower growth in December, pointing to an economy that continues to expand at a modest pace, while factory orders rose in November.
Analysts at BNP Paribas said the reports were not weak enough to call into question the Federal Reserve's plans to continue tapering its asset purchases.
"We expect to see good interest to buy USD on dips heading into the jobs release, and remain short EUR/USD as a trade recommendation," they wrote in a report to clients.
On the daily Ichimoku chart, a popular technical analysis tool, the dollar has support at about 103.53 yen.
"I think most people regard the recent moves including those in equities as just a corrective phase," said Teppei Ino, a Singapore-based analyst for Bank of Tokyo-Mitsubishi UFJ.
"For now, there are a number of (dollar/yen) support levels on technical charts," he added.