* Report of downed fighter jet drives Treasuries buying
* Traders shrug off surprise drop in jobless claims
* Ukraine crisis threatens euro zone economy, Draghi says (Adds price jump, yield records and quotes)
NEW YORK, Aug 7 (Reuters) - U.S. Treasuries prices rose on Thursday, knocking benchmark 10-year yields to lows last seen in May, as a report that a Ukrainian fighter jet had been downed rattled investors already worried over a Russian ban of Western food imports.
Ten-year notes, whose yields topped 2.50 percent on Tuesday, were up 9/32 in price to yield 2.44 percent. The yield touched a low of 2.429 percent, which was the lowest payout on the issue since May 29.
A big jump in Treasury prices, which also took 5-year yields to a four-week low, came on an AFP report of a fighter plane downed in Ukraine, according to financial market sources.
"Even before the intentional tragedy of (Malaysian airliner) MH17, the fighter conflict over the eastern border was worrying the market. Now you have a preview of Russian forces possibly moving across the border," said Jim Vogel, interest rate strategist at FTN Financial in Memphis.
Thirty-year Treasury bonds also jumped and were up 17/32 in price to yield 3.248 percent. The long bond had earlier yielded as little as 3.237 percent.
Shortly after the New York open, Treasuries pared overseas gains as data showed the number of Americans filing new claims for unemployment benefits unexpectedly fell last week.
But Treasuries rose again as European Central Bank President Mario Draghi told reporters in Frankfurt that the Ukraine crisis threatened the euro zone economy.
"Draghi seems to be striking a cautionary note," said Guy LeBas, chief fixed income strategist at Janney Montgomery Scott in Philadelphia.
"The thing to look at is the relative value between U.S. and European rates," LeBas said. "With the German 10-year (yielding) below 1.1 percent, it is easy see why many investors would be interested in the U.S. market."
Ten-year Bund yields dropped 3 basis points on Thursday to a record low 1.07 percent amid fears the Ukrainian crisis and tit-for-tat sanctions with Russia may threaten Europe's fragile economic recovery.
Russia said on Wednesday it would ban all food imports from the United States and all fruit and vegetables from Europe in response to Western sanctions on Moscow.
"The real issue is how the sanctions are going to influence economic activity," LeBas said. "One estimate puts the cost of Russia's refusal to import foreign food at as much as 2 percent. That would have a big negative economic impact." (Reporting by Michael Connor in New York; Editing by Bernadette Baum and Dan Grebler)