* Yen higher versus euro and dollar
* U.S. dollar falls from one-month high vs euro after mixed data
* Market still thin ahead of key event risks this week
By Ian Chua
SYDNEY, Jan 7 (Reuters) - The yen firmed across the board early in Asia on Tuesday as investors took aim at the greenback in the wake of disappointing U.S. data, although many currencies remained in familiar ranges in still thin market conditions.
Trading is usually lacklustre in the first full trading week of the year as investors trickle back to their desks, with position adjustments dominating trade. That helped give some support to the yen, the worst performing major currency in 2013 due to Japan's ultra-loose monetary policy.
Traders are also reluctant to make aggressive moves ahead of major risk events later in the week including closely watched U.S. jobs data and policy meetings at the European Central Bank and Bank of England.
The dollar traded at 104.18 yen, having fallen as far as 103.91, a low not seen since Dec. 23. It continued to pull back from a five-year peak of 105.45 set last week.
The euro also lost ground against the yen, reaching a three-week trough of 141.50 as the common currency retreated further from a five-year high of 145.675 set late last month. It was last at 142.05.
Against the dollar, the euro bounced to $1.3633 from a one-month low of $1.3572 after two measures of activity in the U.S. services sector showed slower growth in December.
Traders said the reports gave some investors an added excuse to take profits on long dollar positions, following the footsteps of currency speculators who had already done so in the week ended Dec. 31.
Analysts at BNP Paribas said the reports weren't 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.
Still, the dollar's decline was broad, even allowing the down beaten Australian dollar to pop back to $0.8966, pulling further away from a three-year trough of $0.8820 plumbed last month.
There is little in the way of market-moving economic data out of Asia on Tuesday leaving the focus on equity markets. Any big falls in Asian stocks could underpin demand for the safe-haven yen.