NEW YORK, July 3 (Reuters) - Benchmark 10-year Treasury yields fell on Wednesday after growing signs of weakness in manufacturing and the jobs market suggested the U.S. economy was slowing.

The ISM Non-Manufacturing index was 48.8 in June, well below the 52.5 consensus and the 53.8 level in May. Initial claims for unemployment rose 238,000 in the week ended June 29, slightly above expectations of 235,000, and up from 234,000 the prior week, the Labor Department said.

Data released earlier in the day by ADP showed private payrolls rose by 150,000 jobs in June, below consensus estimates of an increase of 160,000.

"The economy seems to have weakened at quarter-end," said Bill Adams, chief economist for Comerica Bank.

The Federal Reserve has cited the labor market's resilience in the face of interest rates at nearly two-decade highs as one reason why it has yet to cut rates. Futures markets are pricing in roughly 45 basis points in cumulative rate cuts by the end of the year.

The yield on the benchmark U.S. 10-year Treasury note fell 7.7 basis points to 4.359%. The yield on the 30-year bond fell 8 basis points to 4.529%.

The two-year U.S. Treasury yield, which typically moves in step with interest rate expectations, fell 3.1 basis points to 4.708%.

A closely watched part of the U.S. Treasury yield curve measuring the gap between yields on two- and 10-year Treasury notes, seen as an indicator of economic expectations, was at a negative 35.3 basis points. It had touched its least shallow inversion since May earlier in the week.

The bond market closed at 2 p.m. EDT (1800 GMT) ahead of the July Fourth U.S. Independence Day holiday and will reopen on Friday.

The Fed released the minutes from its June policy meeting at 2 p.m. EDT, in which the majority of participants said the U.S. economy appeared to be gradually cooling. (Reporting by David Randall; editing by Barbara Lewis, Richard Chang and Trevor Hunnicutt)