June 7 (Reuters) -

Benchmark 10-year U.S. Treasury yields posted their biggest daily jump in two months on Friday after data showed that U.S. job growth accelerated far more than expected in May, leading traders to pare back expectations that the Federal Reserve could begin cutting interest rates as soon as September.

Non-farm payrolls increased by 272,000 jobs last month, above the gain of 185,000 expected by economists in a Reuters poll. Wage inflation also climbed, with average hourly earnings rising 0.4% after a 0.2% increase in April.

The unemployment rate, meanwhile, ticked up to 4.0% from 3.9% in April.

"There's no urgency for the Fed to cut if the labor market is firm," said Padhraic Garvey, regional head of research for the Americas at ING. "This is the most important employment print that we get. We just had it, it's bang up to date, and it's pretty strong."

Bonds had rallied heading into the data on Friday as traders bet that the report would reflect a cooling labor market.

Personal consumption expenditures (PCE) price index data last Friday showed that core inflation eased in April, boosting expectations the Fed would cut interest rate two times this year as the economy slows and inflation moderates. Some softer jobs-related data this week added to that view.

"There was definitely the build of a rate-cut optimism play since the core PCE number," Garvey said. Now, "I don't see the justification for going much more to the downside" in yields, he said.

Benchmark 10-year note yields were last up 15 basis points at 4.428%, the biggest one-day basis-point jump since April 10. They got as low as 4.275% on Wednesday, the lowest level since April 1.

Two-year note yields gained 15 basis points to 4.87%, also the largest daily increase since April 10. They fell to 4.716% on Thursday, the lowest level since May 16.

The inversion in the two-year, 10-year Treasury yield curve was little changed on the day at minus 44 basis points.

Traders slashed bets on an initial Fed interest rate cut by September after the jobs data, taking the probability down to just a bit stronger than a toss of the coin, from about the 70% chance that was previously seen.

"The Fed may see these numbers as an obstacle for cutting rates in September because what a strong labor market leads to is a stronger consumer, a consumer that can continue to spend and fuel inflation," said Quincy Krosby, chief global strategist at LPL Financial.

The next major focus for the market will be the consumer price index (CPI) data for May due on Wednesday. That report is likely to drive near-term market expectations of Fed policy.

It will be released just hours before the U.S. central bank concludes its latest two-day policy meeting, when Fed officials will update their economic and interest rate projections.

In recent comments, Fed policymakers have stressed that they will need to see inflation falling back closer to the Fed's 2% annual target for several months before cutting rates.

The U.S. Treasury Department will also sell $119 billion in coupon-bearing supply next week, including $58 billion in three-year notes on Monday, $39 billion in 10-year notes on Tuesday and $22 billion in 30-year bonds on Thursday.

(Reporting By Karen Brettell; Additional reporting by Caroline Valetkevitch; Editing by Chizu Nomiyama, Toby Chopra, David Evans and Paul Simao)