UPDATE 1-Euro zone yield rise resumes as focus shifts to Fed's unwind

* 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 (Updates prices, adds quote)

LONDON, July 11 (Reuters) - Euro zone bond yields resumed their march upwards on Tuesday as focus shifted to the pace of monetary tightening in the world's largest economy and when the U.S. central bank might start unwinding its massive balance sheet.

Yields across the bloc fell on Monday, retracing some of a 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.

The ECB's Benoit Coeure is due to speak on Tuesday but analysts said they are most interested in 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 edged up 1 basis point on Tuesday to 0.55 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.

All other euro zone bond yields were up 1-3 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 Gareth Jones)