* Asian shares turn higher, helped by China services PMI
* China's CSI300 up 0.9 pct, Nikkei gains 0.3 pct
* Dollar bounces off near 8-month low vs basket of currencies
* European bourses seen opening weaker
By Dominic Lau
TOKYO, Oct 8 (Reuters) - Asian shares rose on Tuesday as data showed China's services industry continued to expand, soothing to some extent nerves jarred by fears of a U.S. debt default as the U.S. government shutdown entered a second week.
MSCI's broadest index of Asia-Pacific shares outside Japan reversed early losses to trade up 0.4 percent, while China's CSI300 index climbed 0.9 percent on its first trading day in a week after the National Day holidays.
The lift in short-term sentiment after the September Markit/HSBC services PMI, although the index improved at a slower pace than in the previous month, also helped the dollar to come off near an eight-month low against a basket of currencies.
A few glimmers of hope surfaced in Washington on Monday in the U.S. fiscal standoff, with President Barack Obama saying he would accept a short-term increase in the country's borrowing authority in order to avoid a crisis.
But nothing amounting to a breakthrough was in sight ahead of the Oct. 17 deadline to raise the debt ceiling, which could result in a U.S. debt default if not resolved.
This anxiety helped support gold, while concerns that the political wrangling in Washington will crimp economic growth kept pressure on oil prices.
Financial bookmakers expected major European indexes to open down between 0.3 and 0.5 percent.
"Investors have been reluctant to embrace aggressive risk-off trades because they foresee a relief rally once a deal is made, i.e. when it's clear there won't be a default," analysts at Societe Generale wrote in a note.
"The risk, however, is that we get a toxic deal, one way or the other: the deal could simply raise the debt ceiling a bit, forcing further negotiations ... This would cause policy uncertainty and hurt the economy. Or the deal may include a further tightening of fiscal policy."
China and Japan, the United States's biggest creditors, are increasingly worried the shutdown and standoff over the debt ceiling could wreak havoc on their holdings of trillions of dollars in U.S. Treasury bonds.
U.S. Standard & Poor's 500 e-mini futures dipped 0.1 percent in Asian trade after the cash index ended down 0.9 percent on Monday and dropped for the 10th time in the past 13 sessions. U.S. Treasury futures added 2-1/2 ticks.
Tokyo's Nikkei share average advanced 0.3 percent after earlier hitting a five-week low, though its volatility gauge added 0.5 percent as an indication that investors were not totally off their guard over the U.S. fiscal situation.
The dollar added 0.1 percent to 80.051 against a basket of currencies after slipping 0.2 percent overnight to not far from an eight-month trough touched last week.
Against the yen, the greenback was up 0.4 percent at 97.09 yen after falling as much as 0.2 percent to 96.55 yen, hitting an eight-week low earlier in the Asian session.
It dropped 0.8 percent overnight to mark its biggest decline against the Japanese currency since Sept. 18, when the Federal Reserve shocked investors by deciding to continue its stimulus programme.
"In the shorter-term, with financial sector stress increasingly looking like a necessary ingredient to forcing a negotiated solution in Washington, we think risks lie to the yen upside," analysts at BNP Paribas wrote in a note, though they remained optimistic that the U.S. fiscal crisis will be resolved.
Gold, seen as a safe-haven, gained 0.3 percent to around $1,324.5 an ounce, adding to Monday's 0.8 percent rise, while Brent crude slipped 0.2 percent to $109.4 a barrel.