* Dollar shaky after big falls in previous session ahead of payrolls
* European shares steady, on course for third week of losses
* MSCI Asia ex-Japan falls to fresh six-month lows
* Volatile Nikkei keeps dollar jittery vs yen
By Marc Jones
LONDON, June 7 (Reuters) - The dollar was under pressure on Friday and shares were on track for a third straight week of losses as markets experienced an uneasy run-up to U.S. jobs data later in the session.
The dollar hovered near a 3-1/2 month low against a basket of currencies and was fragile against the yen at 96.37 yen after its biggest fall against the Japanese currency in three years on Thursday.
World and European shares were little changed as they failed to rebound from sharp falls in the previous session which had pushed them to six-week lows. Japanese stocks plunged to two-month lows in Asian trading after their worst week in two years.
That reflected tension ahead of U.S. non-farm payrolls figures due at 1230 GMT, which could influence the Federal Reserve's stimulus programme after talk intensified this week about the Fed scaling it back in the coming months.
Economists polled by Reuters expect to see a 170,000 increase in non-farm payrolls in May, which would be the third straight month that job growth was less than 200,000.
"Over the very short run there might be some relief (from payrolls) but the general theme is that ... we seem to be losing our mantra that central banks will help us all the way," said Gerhard Schwarz, head of equity strategy at Baader Bank.
"We are heading for increased volatility and some kind of topping out process over the next couple of weeks, but at some point probably there will a 10 percent correction coming into the equity market, and possibly deeper into the third quarter."
In the debt market, safe-haven German Bunds edged higher but trade was expected to be choppy going into the U.S. data.
Mario Draghi tempered expectations for imminent European Central Bank rate cuts on Thursday and that was also continuing to boost demand for Bunds as they headed for their first weekly rise in three weeks.
His message had triggered the biggest daily drops in Italian and Spanish bonds and pushed the euro to its highest level against the dollar since February on Thursday, and all hovered near those levels at mid-morning.
Austria's ECB policymaker Ewald Nowotny told reporters it was possible there would be no further ECB moves if the euro zone's economy now picks up as expected.
The euro was last at $1.3242 as it edged back from the previous session's high of $1.3306, while against the stronger yen it was down at $1.3242, having hit its lowest level since mid-April.
The Bundesbank trimmed its German growth forecasts on Friday but there were fresh signs that Europe's largest economy is regaining some momentum after its exports rose in April and imports surged even more.
The sharp fall in the dollar lent support to the prices of a wide range of commodities as it makes them cheaper for holders of other currencies.
"If the jobs data comes in weaker than expected, it may mean the Fed postpones tapering of its quantitative easing which should weigh on the dollar and support metals," said economist Alexandra Knight of National Australia Bank in Melbourne.
Copper, trading on the London Metal Exchange, added 0.1 percent to $7,341 a tonne, while gold was steady at around $1,413 an ounce, with both metals on course for weekly gains.
Brent crude edged above $104 a barrel on track for a weekly gain of 3.4 percent, its best week since late April.