* EM, European shares rise to put world index near one-year high
* AUD climbs on RBA decision to hold rate at record-low 1.5 pct
* Nikkei closes up 0.3 percent as dollar strengthens slightly
* Oil prices in tighter range after $3 move
* Oil gains on Russian, Saudi agreement to stabilize market
By Marc Jones
LONDON, Sept 6 (Reuters) - World shares closed in on one-year highs on Tuesday as the prospect of prolonged cheap borrowing costs and a recent rise in oil prices set off a new emerging market bull run.
Asian stocks reached one-year highs overnight and MSCI's 46-country 'All World' index was close as most of Europe's markets climbed 0.1 to 0.3 percent higher.
Britain's FTSE 100 was the laggard, spending a second day in the red, as sterling's slow recovery after the country voted to leave the European Union left investors looking at companies' competitiveness again.
Emerging markets had no such worries. A gain of nearly 0.8 percent for the main emerging market stock index took its rise over the last three trading days past 3 percent and put it up more than a third since January.
The latest advance came as the prospect of a U.S. interest rate rise was pushed back by weak jobs data on Friday. Rising oil prices helped oil-rich emerging markets such as Mexico, Brazil and Russia. (EM stocks performance in 2016 link.reuters.com/weh36s)
"Emerging markets have continued to rally, supported by a rise in commodity prices and continued expectations that the Fed will remain dovish," said Standard Life Investment's Alex Wolf.
"In addition, there are some fundamental improvements - August sales improved across many companies and PMI data showed stabilization in China."
Oil markets were calmer, after prices surged, then slid on Monday, when Russia and Saudi Arabia confirmed they had agreed to cooperate to stabilise the oil market, although they offered no immediate plan of action.
U.S. crude was up 50 cents at just over $45 a barrel. Brent crude was down at $47.32, having swung from $46.40 to $49.40 the previous session.
The U.S. dollar barely budged against the yen, at 103.67 yen , but fell for a fifth day against the pound and eased to 1.1166 per euro.
Australia's dollar jumped almost 1 percent to $0.7655 after the country's central bank said little on the currency's 10 percent rise since January and kept Aussie interest rates at 1.5 percent.
"One perhaps could have expected some more discussion of the currency, but we probably need to get back above 0.80 for verbal invention to come back into flavour," said Tobias Davis, head of corporate treasury sales with Western Union in London.
Australian shares slipped 0.4 percent after the RBA's decision, but MSCI's broadest index of Asia-Pacific shares outside Japan extended its recent gains to set a new one-year high overnight.
Japan's Nikkei stock index closed up 0.3 percent as the yen gave up some gains from Monday, when Bank of Japan Governor Haruhiko Kuroda shied away from detailed talk of fresh BOJ stimulus.
European bonds were buoyant. Spanish government bond yields slipped below 1 percent, continuing a strong performance that defies growing political uncertainty in Spain. German Bund yields fell to minus 0.059 percent.
For Reuters new Live Markets blog on European and UK stock markets see reuters://realtime/verb=Open/url=http://emea1.apps.cp.extranet.thomsonreuters.biz/cms/?pageId=livemarkets
Additional reporting by Patrick Graham, editing by Larry King