* Spreadbetters see lacklustre starts at European bourses
* Strong US factory data bolsters dollar ahead of jobs report
* Australian central bank holds steady as expected
* Oil gives back some of Monday's gains
By Lisa Twaronite
TOKYO, Oct 4 (Reuters) - Asian shares shrugged off a sluggish start and pushed higher on Tuesday, with Japanese markets leading the way after an upbeat U.S. manufacturing survey bolstered the dollar.
But the cheer was unlikely to spread to Europe, where German markets will reopen after a holiday to rekindled fears about the stability of the country's largest lender.
U.S. stocks slumped overnight, with Deutsche Bank shares resuming their slide as hopes faded that the bank would reach a swift deal with the U.S. Department of Justice over a fine of up to $14 billion for mis-selling mortgage-backed securities.
"The return of German markets today is likely to see Deutsche Bank's shares come under the microscope again after the face-ripping rally on Friday that saw a 14 percent swing in the share price," wrote Michael Hewson, chief market analyst at CMC Markets in London.
Hewson expected Britain's FTSE 100 and Germany's DAX to begin the day modestly lower, and France's CAC 40 to open nearly flat.
MSCI's broadest index of Asia-Pacific shares outside Japan was up 0.2 percent in afternoon trade. Markets in China are on holiday this week.
Australian shares ended 0.1 percent higher after Australia's central bank kept its cash rate steady at 1.5 percent on Tuesday, a widely expected decision as it assesses the impact of its May and August rate cuts.
"We think the case for no more cuts is strengthening," says Paul Bloxham, chief economist Australia at HSBC. "Economic growth is strong, commodity prices have risen, and the drag from the mining investment decline is set to fade."
Japan's Nikkei stock index gained 0.8 percent, getting a tailwind as the dollar rose against the yen after strong U.S. data.
On Monday, the Institute for Supply Management (ISM) said that its index of U.S. national factory activity rose to 51.5 in September from 49.4 in August, indicating that the sector is now expanding.
"The upbeat U.S. survey is lifting expectations for a strong dollar trend, which helps earnings concerns recede for Japanese exporters," said Hikaru Sato, senior technical analyst at Daiwa Securities.
The upbeat U.S. factory numbers had a mixed impact on U.S. shares overnight. While strong survey reassured investors worried about the strength of the U.S. economy, it also emcouraged bets that the Federal Reserve will raise interest rates as early as this year. Higher rates, while good for the dollar, could pressure equities markets.
Fed funds futures imply that investors slightly favour the chance for an interest rate increase in December.
The dollar index, which tracks the greenback against a basket of six major peers, added 0.3 percent to 95.970.
Against the yen, the dollar added 0.6 percent to 102.25 , breaking above the 102 level for the first time since Sept. 21, while the euro was 0.2 percent lower at $1.1187 .
The main economic indicator this week is Friday's nonfarm payrolls report. Employers are expected to have added 170,000 jobs in September, according to the median estimate of 59 economists polled by Reuters.
Sterling nursed losses not far from 31-year lows and was last at $1.2841. The pound plunged after the UK set a March deadline to begin the formal process for Britain's exit from the European Union.
Crude oil futures took a breather following sharp gains overnight as Iran urged other oil producers to join OPEC in supporting the market.
U.S. crude was down 0.6 percent at $48.52 a barrel after closing up 1.2 percent on Monday. Brent was down 0.4 percent at $50.68 after gaining 1.4 percent overnight. (Additional reporting by Wayne Cole in Sydney and Ayai Tomisawa in Tokyo; Editing by Eric Meijer and Simon Cameron-Moore)