NEW YORK, April 9 (Reuters) - U.S. Treasury yields declined on Tuesday because of some buying on dips after a recent sell-off, as bond investors waited for inflation data on Wednesday to gauge the future path of interest rates.

Yields, which move inversely to prices, hit their highest level since November across different maturities on Monday, following a jobs report last week that showed continued economic resilience despite high borrowing costs.

This attracted some buyers, with Treasuries on Tuesday also tracking rising government bond prices in Europe, where the market expects the European Central Bank may this week hint at a first rate cut in June.

"We've had a pretty significant sell-off, so it makes sense to me that people would take some chips back," said Tony Farren, managing director at Mischler Financial Group. "There are some people at the Fed that clearly want to cut rates; I don't know why, but they clearly do," he added.

Federal Reserve Bank of Cleveland President Loretta Mester said last week that she continued to expect the central bank would be able to cut rates later this year. On Tuesday, former St. Louis Fed President James Bullard said in a Bloomberg interview he was still expecting three rate cuts this year, an outlook investors have been questioning over the past few weeks as economic data keeps surprising on the upside.

On the other hand, other Fed officials have in recent days called for caution on rate cuts if inflation stalls out.

In this context, inflation data on Wednesday will be an important piece of the puzzle for investors to assess whether the Fed will be able to lower rates later this year.

"The backstory is that yields have risen reasonably dramatically over the past week or so, and there is a bit of a pause ahead of the CPI (consumer price index data) tomorrow, which is going to be critical," said Padhraic Garvey, regional head of research, Americas at ING.

"There's always an excuse on any given day for yields to test lower because the big carrot is future rate cuts. ... The big stumbling block is just U.S. data, which is not playing ball for the rate cut story," he said.

Fed funds futures traders were betting on about 67 basis points of cuts on Tuesday, below Fed officials' latest projections of a total of 75 basis points in cuts for 2024.

Benchmark 10-year yields were last seen at 4.365%, down from a nearly five-month high of 4.464% on Monday.

Two-year yields, which tend to more closely reflect market expectations for changes in interest rates, were down to 4.747% from 4.789% on Monday, while 30-year yields declined by over 5 basis points to 4.498%.

The Treasury sold $58 billion in three-year notes with a high yield of 4.548%, nearly 2 basis points above the expected rate at the time of the bid deadline, a sign that investors demanded a premium to absorb the issuance.

Three-year yields had declined prior to the debt sale but ticked up higher afterwards and were last seen at 4.557%.

The Treasury will auction 10-year and 30-year paper on Wednesday and Thursday, respectively.

(Reporting by Davide Barbuscia; Editing by Andrea Ricci)