* Dollar index struggles near 8-month trough
* Euro holds firm, not far from this year's peak of $1.3711
* Yen near 5-week high vs dollar, little changed after BOJ
By Anooja Debnath
LONDON, Oct 4 (Reuters) - The dollar struggled near an eightmonth low on Friday as the U.S. government shutdown dragged on,while the euro, boosted by positive euro zone data, held firmwithin striking distance of its 2013 peak.
The dollar was flat at 79.767 against a basket ofcurrencies, not far from the previous session's trough of79.627, its lowest since early February. The dollar was on trackfor its fourth consecutive week of losses.
The euro was flat at $1.3621, having touched a peakof $1.36465 on Thursday, its highest since February when itscaled this year's high of $1.3711. It has risen 0.8 percent onthe dollar so far this week.
The dollar saw little respite this week with marketsconcerned that the U.S. impasse would merge with a more complexfight over raising the U.S. debt limit later this month. Failureto do so may lead to a historic debt default.
Adding to the greenback's woes was data on Thursday thatshowed growth in the U.S. service sector had cooled last month.
"No one wants to touch the dollar while we haveuncertainties regarding the U.S. government shutdown. We alsohad a disappointing service sector number and that also added tothe negative dollar sentiment," said Niels Christensen, FXstrategist at Nordea.
Adding to market uncertainty, the U.S. Labour Department onThursday said the employment report for September will not bereleased as scheduled on Friday due to the government shutdown.No new date was set.
Thus, any confirmation of an improving labour market thatthe Federal Reserve wants to see before cutting its stimulus,will likely be delayed and hurt the dollar. Two senior Fedofficials said monetary policy was being kept easier to helpoffset the harm caused by political fighting.
"Now some people are saying (Fed) tapering will have to waituntil next year," said Katsunori Kitakura, associate manager ofmarket making at Sumitomo Mitsui Trust Bank. "Those who havebeen expecting it in October should be having a bit of panicnow. Those who have bet on December may be worried too."
The dollar's weakness helped support the euro.
The resolution of political turmoil in Italy, the EuropeanCentral Bank sounding less perturbed about the euro's strengthand refraining from any immediate policy action to help theeconomy and positive service sector data from the currency bloc,all supported the euro.
Against the struggling dollar, the yen traded near afive-week high, reacting little to the Bank of Japan's decisionto keep policy on hold as it was expected.
The dollar was down 0.1 percent at 97.12 yen, havingslid to a five-week low of 96.93 yen on Thursday, not far froman important support of its 200-day moving average at 96.63.