May 16 (Reuters) - U.S. Treasury yields rebounded from almost six-week lows on Thursday after data showed jobless claims fell in the latest week and as Federal Reserve officials said they need to see further progress on inflation before cutting interest rates.

Benchmark 10-year yields also bounced after they briefly fell to the 200-day moving average, which is seen as a technical area of support.

The number of Americans filing new claims for jobless benefits fell last week to a seasonally adjusted 222,000, unwinding nearly half of the jump at the start of the month.

The jobs data underscores that the economy is strong enough to allow the Fed to keep rates steady as they wait for more confirmation that inflation will continue to recede.

"Things are still moving along and the Fed is on hold for now, and they claim they are going to be on hold for a while,” said Ellis Phifer, managing director of fixed income research at Raymond James in Memphis, Tennessee.

Bonds rallied earlier on Thursday and yields hit their lowest levels since April 5 as traders boosted bets that the Federal Reserve will cut rates two times this year, with the first cut likely in September.

That followed data on Wednesday showing the consumer price index rose 0.3% last month after advancing 0.4% in March and February. The core CPI rose 0.3% in April after advancing 0.4% for three straight months. “Yesterday’s news was good in the sense that it wasn’t hotter than expected,” said Phifer.

Traders are closely watching inflation for signs that price pressures are moving back closer to the Fed’s 2% annual target. Stronger-than-expected price gains in the first quarter raised doubts that the U.S. central bank will be able to cut rates in the coming months.

Analysts say that while Wednesday's data could give the Fed some confidence inflation is improving, they will need to see further easing in price pressures before cutting rates.

New York Fed President John Williams said that the data is not enough to call for the U.S. central bank to cut interest rates sometime soon.

Richmond Fed President Thomas Barkin also said that inflation is still not where the Fed needs it to be, while Cleveland Fed President Loretta Mester said that holding U.S. central bank policy at current levels will help get still-high inflation back to the 2% target.

Other data on Thursday suggested the economy lost further momentum early in the second quarter with single-family homebuilding falling for the second straight month in April and permits for future construction hitting an eight-month low. Output at factories unexpectedly fell.

Benchmark 10-year yields were last up 2 basis points on the day at 4.377% after earlier falling to 4.313%, the lowest since April 5. They are now trading back above the 200-day moving average of 4.331%, after briefly trading below it.

Two-year yields rose 6 basis points to 4.793% after earlier reaching 4.705%, also the lowest since April 5.

The inversion in the yield curve between two-year and 10-year notes widened 4 basis points on the day to minus 42 basis points.

(Reporting By Karen Brettell; additional reporting by Terence Gabriel; editing by Jonathan Oatis and Lisa Shumaker)