* U.S. ADP report shows jobs gain of 253,000
* U.S. weekly jobless claims rise more than expected
* U.S. construction spending falls, manufacturing up slightly (Adds construction spending, ISM data, other currencies, new comment, updates prices)
By Gertrude Chavez-Dreyfuss
NEW YORK, June 1 (Reuters) - The dollar rallied on Thursday after a report showed the U.S. economy created more private sector jobs than expected in May, bolstering expectations for an interest rate hike this month.
The U.S. unit hit session highs against major currencies such as the yen, euro, and Swiss franc following the jobs report, although it already traded higher ahead of the data following losses this week.
The private sector employment report by payrolls processor ADP showed employers added 253,000 jobs last month. Economists surveyed by Reuters had forecast the ADP report would show a gain of 185,000 jobs.
Interest rate futures after the data priced in a 96 percent chance the Federal Reserve would hike rates in June.
Still, some analysts were skeptical about the ADP figures.
"Take this morning's estimate from ADP...with a huge grain of salt," said John Herrmann, rates strategist at MUFG Securities Americas in New York.
If the ADP's estimate of 253,000 jobs gained on a seasonally adjusted basis were accurate, then on a non-seasonally adjusted basis, the raw gain in private payrolls in May would have to be 996,000 jobs based on MUFG's models.
"Such a 996,000 month-on-month gain would be the third strongest May monthly gain in history."
Hermann said that kind of private jobs gain was unrealistic.
In late morning trading, the dollar rose 0.4 percent to 111.25 yen, while the euro fell 0.1 percent to $1.1223 .
A report showing U.S. weekly jobless claims rising more than expected to 248,000 hardly mattered as investors focused on the strong ADP data.
Other data on Friday included a drop in U.S. construction spending in April of 1.4 percent, the largest fall in a year. That, however, was offset by a fairly positive U.S. manufacturing report from the Institute for Supply Management, which showed its index edging up to 54.9 with gains in the employment and new orders components.
"The inconsistency in today's data is part of a larger trend as the U.S. economy continues to chug along near full employment, yet inflation remains subdued," said Sean Coakley, market strategist at Cambridge Global Payments in Vancouver.
"Meanwhile, the doves at the Fed peck away at any rationale to maintain a moderate pace of interest-rate normalization."
The dollar index was last up 0.2 percent at 97.12
Reporting by Gertrude Chavez-Dreyfuss; Editing by Andrea Ricci