UPDATE 1-Undercurrent of risk pushes euro zone bond yields lower

* Investors take cue from policymaker caution on recovery

* German bond yields well below recent highs at 0.36 pct

* Political hurdles remain after French election

* Euro zone periphery bond yields http://tmsnrt.rs/2ii2Bqr (Adds quote, updates prices)

LONDON, May 26 (Reuters) - An undercurrent of political and policy risks pushed down euro zone government bond yields on Friday, discouraging investors from putting too much faith in improved economic data.

Despite a market-friendly result in the French presidential election and strong recent inflation and private sector activity numbers from the bloc, most euro zone bond yields are well below recent highs.

Germany's 10-year government bond yield, the benchmark for the region, fell 3 basis point to a one-week low of 0.33 percent -- comfortably above the 0.20 percent level at the start of the year but well below the 0.51 percent March high.

Other euro zone yields were 2-4 bps lower on the day, with Belgium's 10-year yield hitting a three-month low of 0.695 percent.

Investors took their cue from policymakers staying cautious on the brightening political and economic picture in Europe and its implications for monetary policy.

"We have had a few positive political outcomes, but we still have Brexit negotiations to come, Italian and German elections, a potential Catalonia (independence) referendum and the unpredictable factor of Donald Trump's presidency," ING strategist Padhraic Garvey said.

"So even though we are moving towards higher rates in the U.S. and tapering in Europe, in general policymakers are being very careful."

This was underlined this week when top European Central Bank officials made it clear they would not favour changing the policy path they had already outlined.

U.S. Federal Reserve minutes this week showed policymakers agreed to hold off on raising interest rates until it was clear a recent U.S. economic slowdown was temporary.

Expectations the Fed will run down its balance sheet were also exerting downward pressure on yields, said Rabobank strategist Richard McGuire.

"As the Fed appears to be on course on balance sheet normalisation, that possibly adds to the bullish outlook for U.S. Treasuries as they presumably won't hike rates at the same time they are reducing the balance sheet," he said.

Ten-year U.S. Treasury yields dropped 2 basis points to 2.235 percent while volatility in Treasuries hit a 3-year low, after the minutes signalled a steady, predictable balance sheet rundown.

A survey showed this week that businesses across the euro zone maintained April's strong growth rate in May, pointing to 0.7 percent economic growth in the second quarter.

"Certainly this is a positive assessments of the way the euro zone economy is heading, but you could say the surveys are running ahead of the hard data," said Investec economist Philip Shaw. "There is still a degree of scepticism."

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(Reporting by Abhinav Ramnarayan; Editing by Angus MacSwan and John Stonestreet)