TREASURIES-Prices rally on record low increase in Q2 labor costs

* U.S. Employment Cost Index barely rises in Q2

* Smallest increase in ECI in 33-year history of index

* Argument for Fed September rate rise takes a blow

* U.S. fund managers increase bond exposure

By Daniel Bases

NEW YORK, July 31 (Reuters) - U.S. Treasuries rallied on Friday after data showed labor costs rose in the second quarter by the smallest margin on record, putting a dent in the argument for the U.S. Federal Reserve to raise interest rates in September.

Investors have been building positions that anticipated the Fed this year will finally raise U.S. interest for the first time since 2006, lifting off its near-zero interest rate policy as the economy strengthens.

The Employment Cost Index (ECI), the broadest measure of labor costs, rose 0.2 percent, marking the smallest increase in the index's 33-year history, the U.S. Labor Department reported.

"The magnitude of the miss was definitely a bit of a surprise, especially as people were really gearing up for a September (rate) hike. This definitely puts a lower probability on that," said Stanley Sun, interest rate strategist at Nomura Securities International in New York.

"The fact that most people were not expecting this number to be such a big miss caused them to be caught on the wrong side of the trade and the rally to be bigger than expected. It is really the ECI today rather than other data that is important because the Fed is looking at that number," Sun said.

Other economic data were mixed. Business activity in the U.S. Midwest hit a six-month high in July, topping forecasts, while the final reading of the July University of Michigan consumer sentiment survey fell.

"Recent reports have given Fed doves all the talking points they'll need if they opt to delay a September hike in rates, though we continue to assume a September move," wrote Mike Englund, chief economist at Action Economics in Boulder, Colorado.

Even (Taiwan OTC: 6436.TWO - news) with the Fed poised to raise rates, U.S. fund managers increased bond exposure in their model global portfolios in July. Fund managers in the latest Reuters global survey trimmed overall allocations to U.S. and Canadian fixed income, but increased exposure to euro zone debt.

The two-year Treasury note yield fell to a low of 0.6610 percent from 0.7398 after the ECI data. It last traded around 0.6724 percent, up 4/32 of a point in price.

Benchmark 10-year Treasury yields fell to a three-week low of 2.1930 percent, the price up 20/32 of a point.

The 30-year Treasury popped higher, rising more than a full point in price, driving the yield down to a fresh two-month nadir of 2.8950 percent. It was last up 31/32 of a point, yielding 2.9038 percent.

(Editing by Bernadette Baum and Meredith Mazzilli)