NEW YORK, June 14 (Reuters) - Longer-dated U.S. Treasury yields edged lower on Friday, after economic data provided the latest indication that inflation may be cooling, with the benchmark 10-year Treasury yield on pace for its biggest weekly drop of the year.

The Labor Department said U.S. import prices dropped 0.4% last month, below the estimate for a 0.1% rise, following an unrevised 0.9% jump in April as prices for energy products retreated, another positive sign for the inflation outlook.

The report comes after data earlier this week indicated the labor market and price pressures were showing signs of cooling.

A separate preliminary reading of consumer sentiment from the University of Michigan showed June was weaker than expected and below the final reading for May, while inflation worries remained despite the drop in energy prices.

"We are now resuming the trend of moderating inflation, but clearly after 1Q disappointments the Fed doesn't want to come across as saying that the battle is won, we can now proceed with cutting rates without having more confirmation that this recent improvement in inflation trends are here to stay," said Andrzej Skiba, head of the BlueBay U.S. fixed income team at RBC Global Asset Management in Stamford, Connecticut.

"We do not see a reason why September could not be the month where they cut for the first time but again, they need to see a few more decent inflation prints to get that confidence."

The yield on the benchmark U.S. 10-year Treasury note fell 2.3 basis points (bps) to 4.217%. The yield is down nearly 22 bps on the week, on track for its biggest weekly fall since mid-December.

On Wednesday, the Federal Reserve held interest rates steady on Wednesday and pushed out the start of rate cuts to perhaps as late as December.

Skiba also said concerns about the upcoming parliamentary election in France was weighing on yields.

The yield on the 30-year bond fell 5 basis points to 4.351%.

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 47.7 basis points.

The two-year U.S. Treasury yield, which typically moves in step with interest rate expectations, rose 0.4 basis points to 4.692%.

Federal Reserve Bank of Cleveland President Loretta Mester said in an interview on CNBC that the latest round of inflation data is good news for the economy and the central bank.

Those comments were echoed by Chicago Fed President Austan Goolsbee, who said, "We would be feeling very good" if there were a lot more months like May.

Markets are pricing in 69.2% chance for a cut of at least 25 basis at the Fed's September meeting, according to CME's

FedWatch Tool

, up from about 50% a week ago.

Fed Governor Lisa Cook is set to speak later on Friday.

The breakeven rate on five-year U.S. Treasury Inflation-Protected Securities (TIPS) was last at 2.136% after closing at 2.166% on June 13.

The 10-year TIPS breakeven rate was last at 2.185%, indicating the market sees inflation averaging about 2.2% a year for the next decade.

(Reporting by Chuck Mikolajczak, Editing by Franklin Paul and Cynthia Osterman)