* Fed's Brainard to speak on normalising balance sheet
* Yellen due to give semi-annual testimony on Wednesday
* ESM urges Greece to ready market borrowing strategy
* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr (Adds Coeure quotes, updates prices)
LONDON, July 11 (Reuters) - Euro zone bond yields resumed their rise on Tuesday as focus shifted to the pace of monetary tightening in the United States and when the Federal Reserve might start unwinding its massive balance sheet.
Yields across the bloc fell on Monday, retracing some of the sharp rise seen over the last two weeks in which the benchmark German 10-year yield has more than doubled on the growing view that the European Central Bank will begin reining in its ultra-loose policy sooner rather than later.
They remained under upward pressure after ECB director Benoit Coeure said on Tuesday that a weaker euro is neither a means nor a goal of the central bank's massive bond purchases.
Analysts said they were also looking ahead to a speech by Fed Governor Lael Brainard on the topic of normalising central banks' balance sheets, while Fed chair Janet Yellen's semi-annual testimony to Congress follows on Wednesday.
San Francisco Federal Reserve Bank President John Williams said earlier on Tuesday in Sydney that he expected the Fed to start unwinding its massive balance sheet in the next few months and for it to raise rates one more time this year.
"Given the recent sensitivity to central bank talk about unwinding emergency stimulus, today's speech by the Fed's Brainard... looks like a compelling read before Yellen's testimony moves into focus tomorrow," said Padhraic Garvey, global head of debt and rates strategy at ING.
Germany's 10-year yield was up 2 basis points on Tuesday at 0.56 percent, reversing some of a near 4 basis point fall on Monday, which was the biggest daily drop in around a month.
That drop appears to have been just a pause in a sell-off that has seen Germany's 10-year yield more than double from the 0.25 percent it was at on June 27, the day ECB President Mario Draghi hinted at the possibility of tweaking the central bank's aggressive stimulus in a speech in Sintra, Portugal.
The yield remains within touching distance of an 18-month high of 0.583 percent hit in early trading on Monday.
Other euro zone bond yields were up 1-4 bps on the day.
"The concerted global pivot toward reduced monetary policy stimulus has left investors needing to balance the improved attractiveness of government bond yields after the recent selloff with anxiety over portfolio vulnerability to renewed selling pressures as central banks scale back liquidity," said Lena Komileva, managing director at G+ Economics.
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(Editing by Jeremy Gaunt)