UPDATE 1-Periphery leads euro zone bond yields down as flash PMI dips

* Euro zone flash composite PMI dips

* Bond yields lower, reverse early rise

* Mersch: unlikely that easy policy will remain too long

* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr (Recasts)

LONDON, July 24 (Reuters) - Bond yields in Italy and Portugal hit their lowest levels in around a month on Monday, leading a fall in euro zone borrowing costs as signs of slowing growth in business activity reaffirmed a view that any unwinding of ECB stimulus is likely to be slow.

In the past week, comments from the European Central Bank and strength in the euro - trading near two-year highs against the dollar - have eased investor worries about a tapering of the central bank's bond-buying stimulus scheme.

Data on Monday showing Germany's private sector grew at a slower pace in July, while French business activity slowed more than expected in July to a six-month low gave investors another incentive to move back into bond markets that have been rattled in the past month by concerns over tapering.

Portugal's 10-year government bond yield fell 5 basis points to 2.89 percent, its lowest level in just over a month. Italian 10-year bond yields were down 4 bps at 2.04 percent - their lowest in almost a month.

"Sentiment is still very positive after the ECB sounded dovish at last week's meeting," said Benjamin Schroeder, a rates strategist at ING. "It doesn't look like there is an urgent need to tweak policy."

Appetite for the region's riskier markets was also boosted by positive ratings news on Friday.

S&P revised the ratings outlook for Greece to "positive" from "stable", citing an expectation that debt levels will decline. Fitch raised the outlook on Spain's BBB+ rating to "positive" from "stable".

Other euro zone bond yields were 1-2 bps lower on the day, with Germany's benchmark 10-year Bund yield dipping to its lowest level in just over at week at 0.49 percent.

It had opened the day higher, with analysts citing an upward revision in International Monetary Fund growth forecasts for the euro area as a reason for initial weakness in bond markets. When a bond yield rises, its price falls.

In an updated World Economic Outlook on Monday, the IMF upgraded its 2017 gross domestic product (GDP) growth projection for the euro zone to 1.9 percent, up 0.2 percentage point from April, and pointed to "solid momentum".

It shaved its forecasts for U.S. economic growth and cut its 2017 GDP forecast for Britain.

ECB board member Yves Mersch said on Monday unconventional monetary policy tools used since the global financial crisis were unlikely to remain necessary as the global economy and central banking normalise.

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

(Reporting by Dhara Ranasinghe; Editing by Alison Williams)