(Adds Bund record low, updates prices)
By Dhara Ranasinghe and Nigel Stephenson
LONDON, June 7 (Reuters) - Germany's 10-year Bund yield fell to a new record low on Tuesday, against a backdrop of nervousness about Britain's referendum on EU membership and unprecedented monetary stimulus from the European Central Bank.
The Bund yield, the benchmark for euro zone borrowing costs, fell as low as 0.045 percent, according to Tradeweb data. This took it below the previous record low of 0.05 percent hit on April 17, 2015.
Yields on the ultra-low risk Bund are expected to stay close to current levels as Britain's June 23 vote on whether to stay in the European Union approaches.
"Everyone knows no dealer wants to be short Bunds into the referendum," said Commerzbank rates strategist Christoph Rieger.
Uncertainty about the outcome of the referendum and its implications for the euro zone are boosting demand for German bonds - deemed one of the safest assets in the world.
"There are a number of reasons why you can't be short Bunds right now," said Mizuho strategist Peter Chatwell. "Number 1 is the UK referendum and political risks in the euro zone."
In addition, Spain votes on June 26 in a re-run of an inconclusive December election. And last weekend, the anti-establishment 5-Star Movement made headway in local elections in Italy - piling pressure on Prime Minister Matteo Renzi.
Brexit jitters, while boosting demand for German bonds, are weighing on peripheral bonds that are seen as especially vulnerable.
"We could see talk of more countries leaving the euro zone, so Europe could suffer more than the UK," said Patrick Zweifel, chief economist at Pictet Asset Management.
Italian yields notched up their biggest one-day rise in six weeks and Portuguese yields hit a three-week high on Monday on Brexit fears and Italy's election results.
But peripheral bonds were on a firmer footing on Tuesday after dovish comments from U.S. Federal Reserve Chair Janet Yellen.
Italian, Spanish and Portuguese 10-year yields fell around 4-6 basis points.
In addition to political risks, the European Central Bank's 1.74 trillion euro asset-purchase programme has helped depress bond yields. The average yield of German bonds in circulation dipped to minus 0.02 percent on Monday, falling below zero for the first time, according to data from the German Bundesbank. The average yield stood at minus 0.01 percent on Tuesday.
Data on Monday showed the ECB, faced with a scarcity of eligible bonds, bought more German, French and Italian government debt than its rules dictate in May.
The ECB is due to begin buying corporate debt under the programnme from Wdnesday.
(Editing by Gareth Jones)