* U.S. nonfarm payrolls growth beat expectations
* U.S. unemployment rate hits near six-year low
* Yields fall from highs to trade slightly higher
* ECB's Draghi says rates to stay low (Updates prices, adds comments)
By Sam Forgione
NEW YORK, July 3 (Reuters) - U.S. benchmark Treasuries yields eased from two-month highs on Thursday to trade slightly higher after traders reconsidered a strong U.S. June nonfarm payrolls report and reacted to comments from European Central Bank chief Mario Draghi.
Nonfarm payrolls increased by 288,000 jobs, the Labor Department said on Thursday, where economists polled by Reuters had forecast a gain of 212,000. It was the first time since the technology boom in the late 1990s that employment has grown above a 200,000 pace for five straight months.
The unemployment rate declined to near a six-year low of 6.1 percent.
"This was an exceptionally strong report," said Stan Shipley, senior managing director of fixed income strategy at ISI Group in New York. He said, however, that traders grew complacent to the report after a strong ADP private-sector employment report Wednesday.
Analysts also said yields fell from their highs on uncertainty as to whether U.S. economic growth will meet stronger expectations after the Federal Reserve concludes its monthly bond-buying program and on comments from Draghi.
Many expect the Fed to end its massive asset purchases in October. Draghi said on Thursday that risks facing the euro zone economy meant interest rates there will stay low for an extended period.
The comments stoked some demand for higher U.S. Treasuries yields compared to German 10-year bund yields, which are currently at 1.3 percent, analysts said.
"Draghi's comments increased the attractiveness of Treasuries relative to Bunds and other European debt," said Kim Rupert, managing director of global fixed income at Action Economics in San Francisco.
The Institute for Supply Management said its U.S. services sector activity index ticked down to 56.0 last month from 56.3 in May, which was a nine-month high. The reading fell shy of economists' forecasts for 56.3, according to a Reuters survey, but failed to impact Treasuries prices.
Benchmark 10-year Treasury notes were last down 3/32 in price to yield 2.64 percent, from a yield of 2.63 percent late Wednesday. U.S. 30-year Treasury bonds were last down 1/32 in price to yield 3.47 percent, from a yield of 3.47 percent late Wednesday.
The U.S. 10-year yield hit a two-month high of 2.69 percent, while the 30-year yield hit a two-month high of 3.52 percent following the jobs data. U.S. 2-year Treasury notes were down just 1/32 to yield 0.51 percent after earlier hitting a near nine-month high of 0.53 percent.
On Wall Street, the holiday-shortened session ended with both the Dow and the benchmark S&P 500 at their third consecutive record highs. The S&P 500 closed up 0.55 percent. (Reporting by Sam Forgione; Editing by James Dalgleish and Chizu Nomiyama)