NEW YORK, July 3 (Reuters) - Benchmark 10-year Treasury yields dipped Wednesday after slightly higher than expected jobless claims data suggested that the labor market was softening.

Initial claims for unemployment rose 238,000 the week that ended June 29, slightly above expectations of 235,000, and up from 234,000 the prior week, the Labor Department said.

The rising jobless claims followed data released earlier in the day by ADP that showed private payrolls increased by 150,000 jobs in June, below consensus estimates of an increase of 160,000 jobs.

The labor market's resilience in the face of interest rates at nearly two-decade highs has been cited by the Federal Reserve 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 2.4 basis points to 4.412%. The yield on the 30-year bond fell 3.8 basis points to 4.571%.

The two-year U.S. Treasury yield, which typically moves in step with interest rate expectations, rose 1.7 basis points to 4.756%.

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 34.6 basis points. It had touched its least shallow inversion since May earlier in the week. (Reporting by David Randall; editing by Barbara Lewis)