* Yen near 5-week high vs dollar, little changed after BOJ

* Euro holds firm, not far from this year's peak of $1.3711

* U.S. budget woes keeping dollar pinned down

By Ian Chua and Hideyuki Sano

SYDNEY/TOKYO, Oct 4 (Reuters) - The euro held firm within a striking distance of its 2013 peak on Friday, thanks to a flow of encouraging euro zone data at a time when a U.S. government shutdown is keeping the dollar pinned at eight-month lows.

The yen, in a muted response, stayed near a five-week high against the dollar after the Bank of Japan kept its policy on hold, as expected.

The common currency last traded at $1.3630, flat in Asia after stretching as far as $1.3646 overnight, a level not seen since early February when it scaled this year's peak of $1.3711. It has risen 0.8 percent on the dollar so far this week.

A number of factors supported the euro, not least of them a survey showing Italy's services sector unexpectedly grew in September for the first time in more than two years.

In contrast, growth in the massive U.S. service sector cooled last month, making for an uncomfortable reading just as the shutdown in Washington is fuelling concerns of wider economic consequences.

Fears are also growing that the current impasse would merge with a much more complex fight looming later this month over raising the U.S. debt limit. Failure to do so may lead to a historic debt default.

Although market players expect a last minute deal to avoid such an embarrassing and potentially catastrophic outcome, their nerves are getting frayed.

"Once the market starts to think the unthinkable might happen, then the dollar could dive. The market is getting worried a little," said Katsunori Kitakura, associate manager of market making at Sumitomo Mitsui Trust Bank.

The U.S. Labor Department on Thursday said the employment report for September will not be released as scheduled on Friday due to the government shutdown. It said a new release date had not been set.

This suggests any confirmation of an improving labour market that the Federal Reserve wants to see before cutting its stimulus will likely be delayed, undermining the case for dollar bulls.

"Now some people are saying tapering will have to wait until next year," said Kitakura of Sumitomo Mitsui "Those who have been expecting it in October should be having a bit of panic now. Those who have bet on December may be worried too."

The dollar index, which tracks its performance against a currency basket, wallowed at an eight-month low, having shed 0.7 percent this week.

Two senior Fed officials warned of damaging consequences if the U.S. defaults on its debt and said monetary policy was being kept easier to help offset the harm caused by political fighting.