(Corrects paragraph 2 to ... The yen trimmed its gains...not losses)
* Dollar dips vs yen and euro as risk aversion eases
* Friday's U.S. jobs data not as bad as some had feared
* Dollar index off last week's three-year peak
* Japan record current account deficit in Jan weighs on yen
By Masayuki Kitano
TOKYO, March 9 (Reuters) - The dollar dipped against the euro on Monday as investors trimmed safe-haven buying of the dollar after last week's U.S. payrolls data showed that job losses were less severe than many had feared.
The yen trimmed its gains versus the dollar and dipped against the euro, weighed down by data showing that Japan posted a record current account deficit of 172.8 billion yen ($1.76 billion) in January.
That follows data released last month that showed that Japan posted a record trade deficit in January, the fourth straight month the trade balance registered a deficit.
While initial market reaction to the current account data had been subdued, the yen gradually retreated against the dollar and the euro.
"There has been some gradual selling of the yen, and market sentiment still seems to favour yen-selling," said Osamu Takashima, chief analyst for Bank of Tokyo-Mitsubishi UFJ.
"The fundamental reason may be that the market is still not quite neutral in its positioning, although it may be getting very close to it," he added. Market players may still have some long yen positions that could be unwound, Takashima said.
The euro rose 0.3 percent to $1.2675 and also edged up 0.1 percent against the yen to 124.48 yen.
The dollar dipped 0.2 percent against the yen to 98.21 yen, but was above the day's low of 97.90 yen hit on trading platform EBS earlier.
Latest data shows that currency speculators on the Chicago Mercantile Exchange's International Monetary Market still held net long positions in the yen, although such positions fell to 20,070 contracts in the week ending March 3, from 28,635 the prior week.
DOLLAR SLIPS
Data showed on Friday that U.S. unemployment rate rose to a 25-year high of 8.1 percent in February as employers cut 651,000 jobs.
The fall in payrolls was not as bad as the market's worst expectations, and the data pressured the dollar on Friday.
The dollar is still viewed as a safe-haven currency and tends to attract buying when worries about the global economy and financial markets flare up, but can come under pressure when such concerns recede.
"Ahead of the jobs report there had been rumours about a possible loss of 1 million jobs, but the result turned out to be basically in line with expectations," said a trader for a Japanese trust bank.
Market players said the dollar may start to lose some steam, after hitting a three-year high against a basket of major currencies last week. With the euro starting to look like it is finding some support at levels near $1.2500, and oil looking like it may be poised for a break higher on technical charts, there are some tentative signs of the dollar's rally losing steam, said a trader for a Japanese brokerage house.
"Once market players are done with their dollar buying due to risk aversion, you are not going to see the dollar being bought unless there is a switch to a positive form of dollar buying," he added.
The dollar index stood at 88.416, having retreated from a three-year peak of 89.624 hit last week. (Editing by Edwina Gibbs)