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UPDATE 2-Fed's inflation conundrum firms demand for government bonds

* Some Fed members call for halt in rate hikes

* Trump dissolves business panel adding to economic fears

* Euro zone, U.S. yields fall from one-week peak

* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr (Updates prices, adds quote)

LONDON, Aug 17 (Reuters) - Most euro zone government bond yields fell on Thursday, tracking an earlier move in U.S. Treasuries after minutes of the Federal Reserve's last meeting showed some policymakers called for halting interest rate hikes until inflation improves.

Details of the July meeting, released late on Wednesday, showed concerns that recent soft inflation data may cool the pace of monetary tightening in the world's largest economy despite moderate growth and very low unemployment.

The Fed has raised its benchmark overnight lending rate twice this year and forecasts one more rise before the end of 2017. But money market pricing suggests investors now see less than a 50 percent chance of a hike by December.

"Fed communications are cementing expectations of a very gradual approach to monetary tightening," Mizuho's head of euro rates strategy Peter Chatwell said.

Signs of the central bank's caution came as President Donald Trump dissolved two business advisory group, sowing further doubts over his ability to deliver growth-boosting spending plans he promised when elected.

The Fed is not the only central bank wary of weak inflation.

Reuters reported on Wednesday that European Central Bank President Mario Draghi will not deliver a new policy message at next week's Jackson Hole conference, tempering expectations for the bank to start charting its course out of stimulus.

U.S. 10-year yields, which had climbed to one-week peaks earlier on Wednesday, fell after the minutes and eventually closed down 4 basis points on the day at around 2.23 percent .

When European markets opened on Thursday, benchmark German equivalents fell as much as 2 basis points to 0.42 percent , moving away from Wednesday's high of 0.47 percent. Most other euro zone yields fell 1 bps.

In an interview with Reuters on Wednesday, Cleveland Fed President Loretta Mester staked out the hawkish argument for carrying on with U.S. interest rate hikes even while weak inflation has split opinions among her colleagues.

She said while some price readings have fallen this year, expectations are more stable, and that policy must anticipate changes in the data and not react to temporary aberrations.

San Francisco Federal Reserve President John Williams, a non-voter, said the Fed is roughly at the mid-point on its current path to normalize interest rates. The Fed has raised key overnight borrowing costs four times since December 2015.

The ECB is set to publish minutes of its last meeting later on Thursday, but analysts are not expecting any market-moving revelations.

"Those looking for clues ... on either the ECB's strategy for tapering purchases ... or when it is likely to make an announcement on its plans are likely to be disappointed," RBC's global macro strategist Peter Schaffrik said.

For Reuters Live Markets blog on European and UK stock markets see reuters://realtime/verb=Open/url=http://emea1.apps.cp.extranet.thomsonreuters.bi z / c m s / ? p a g e I d = l i v e m a r k e t s

(Editing by Matthew Mpoke Bigg)