(Updates prices, adds quote, details)
* U.S. ISM manufacturing rises but offset by construction data
* Traders cite selling of T-bond puts
* Focus on Friday's U.S. nonfarm payrolls report
NEW YORK, May 1 (Reuters) - U.S. Treasury debt prices rallied on Thursday, pushing yields on long-dated bonds to multi-month lows, in a market that continued to cover short positions ahead of Friday's all-important U.S. nonfarm payrolls data.
Yields on 30-year bonds plunged to near 11-month lows, while those on 10-year notes slid to two-month troughs.
Thursday's U.S. economic reports were in general positive, which should suggest that Treasuries should sell off, not rally.
On Thursday, the Institute for Supply Management said its index of national factory activity rose to 54.9 in April from 53.7 in March. It was the strongest reading since December. However, that was offset by a lower-than-expected rise in U.S. construction spending of 0.2 percent, compared with expectations for a 0.5 percent increase.
"The fact that we have seen stocks pull back and Treasuries rally despite a strong ISM number would suggest that the market is positioned relatively short for the payrolls number tomorrow," said Ian Lyngen, senior government bond strategist, at CRT Capital in Stamford, Connecticut.
Some analysts were perplexed as to why the bond market reacted more to the construction number, which was backward-looking, instead of the ISM report, viewed as first-tier data.
Lyngen surmised the tepid rebound in U.S. construction spending could further revise lower the already dismal U.S. gross domestic product growth figures for the first quarter.
Ahead of the Labor Department's nonfarm payrolls report on Friday, the market's positioning remained on the short side, analysts said, with volumes light due to the May Day holiday in Europe and much of Asia.
A Reuters poll showed economists expect the U.S. economy to have created 210,000 jobs in April.
In afternoon trading, the benchmark 10-year U.S. Treasury note rose 11/32 in price to yield 2.60 percent, compared to 2.65 percent late on Wednesday. Yields fell as low as 2.59 percent, the lowest since March 3.
Prices of 30-year Treasury bonds were up 28/32 to yield 3.40 percent, from 3.46 percent the previous session. Yields dropped to 3.39 percent, the lowest since mid-June 2013.
Traders also cited selling in U.S. Treasury options on Thursday, as some market participants further reduced their bets of a solid April payrolls figure given Wednesday's poor 0.1 percent reading for first-quarter U.S. GDP growth.
On the Chicago Board of Trade, there was active selling in June T-bond puts at strike prices of 132 and 134 . June T-bond futures rose to 135-15/32 after touching their highest levels in two months earlier.
"There's a bit of a short squeeze here," said John Brady, managing director of interest rate futures sales at R.J. O'Brien and Associates in Chicago. "The economy is not that strong after the GDP, housing and construction numbers we've seen."
Earlier in the session, Treasury prices trimmed losses after data showed U.S. consumer spending in March recorded its largest increase in more than four and a half years, rising 0.9 percent.
A separate report showed initial jobless claims increased 14,000 to a seasonally adjusted 344,000, higher than expected. Still, the overall trend in initial claims continued to point to an improving labor market.
(Additional reporting by Richard Leong; Editing by James Dalgleish)