UPDATE 1-Economic upturn, energy to lift farm prices-FAO/OECD

* 2010-19 agricultural prices seen above 1997-2006 average

* Prices prone to volatility, energy an increasing factor

* FAO says farm investment needs to reach poor countries

(Updates with Gurria, Diouf quotes, farm-sector investment)

By Gus Trompiz

ROME, June 15 (Reuters) - Economic recovery and rising energy costs will lift world agricultural prices in the next decade, but prices will fall short of peaks in 2007-2008, the UN's Food and Agriculture Organisation and OECD said on Tuesday.

"Let's say it's now moving at a more cruising speed," Organisation for Economic Cooperation and Development Secretary-General Angel Gurria said of the outlook for prices.

The price rises would be positive, he said, as it would encourage investments needed to meet rising food demand and cut global hunger.