Private data hints US building rebound continued in May

* Sageworks says privately held builder sales rose in May

* Report suggests US construction rebound may have legs

CHICAGO, June 1 (Reuters) - A private research firm released data on Monday that offered tantalizing hope a two-month rebound in construction activity reported earlier in the day by the U.S. government extended into a third month in May.

Sageworks Inc, a financial information firm that tracks the financials of thousands of privately held U.S. companies, said builders in its database reported their sales rose 4.55 percent in May after rising 2.94 percent in April and 1.66 percent in March.

That resulted in the first rise in Sageworks' measure of trailing three-month construction sales in six months.

"We think the trend is pretty significant," said Dan Saklad, chief operating officer at Sageworks.

Sageworks released the data after the U.S. Commerce Department reported that construction spending rose for a second straight month in April -- and posted its biggest increase in eight months -- as the private sector put money into both residential and nonresidential projects.

Any sustained rebound would be welcome news to construction machinery makers like Caterpillar Inc (CAT.N), Deere & Co (DE.N) and Terex Corp (TEX.N), which have seen their sales -- and share prices -- drop dramatically as a result of the bursting of the U.S. housing bubble.

The downturn in construction spending that has followed has been the worst in at least 40 years and has resulted in the loss of at least 1.36 million jobs in the construction trades, according to the Bureau of Labor Statistics.

Shares of Caterpillar, Deere and Terex rallied strongly on Monday after the Commerce Department numbers were released. (Reporting by James Kelleher; Editing by Steve Orlofsky)