NEW YORK, July 1 (Reuters) - Benchmark 10-year Treasury yields rose to their highest levels since late May on Monday at the start of a holiday-shortened week that will likely be marked by low trading volumes.

The jump in yields, which move inversely to prices, came after the first round of voting in France's national elections on Sunday suggested that Marine Le Pen's National Rally (RN) scored a smaller win than some polls had expected.

At the same time, U.S. President Joe Biden's widely panned debate performance last week may be prompting investors to price in a greater likelihood that former President Donald Trump will prevail in the November election, putting extra pressure on Treasuries, said Thierry Wizman, global forex & rates strategist at Macquarie Group.

"For a variety of reasons having to do with fiscal policy, tariff policy, and immigration policy, we do believe that a prospective Trump administration in 2025-2028 will be more inflationary than a Biden administration," he said.

The selloff in the longer end of the curve suggested that the move was not related to concerns about the Federal Reserve or inflation, but reflecting concerns about rising budget deficits under a second Trump administration, said Lawrence Gillum, Chief Fixed Income Strategist for LPL Financial.

"There’s some election anxiety that’s being brought into the markets with the increase in the odds of Trump winning the presidency," he said.

The yield on the benchmark U.S. 10-year Treasury note rose 13.4 basis points to 4.477%. The yield on the 30-year bond rose 14 basis points to 4.642%.

Ten-year Treasury yields pulled back briefly following a reading by the Institute for Supply Management that showed U.S. manufacturing contracted for a third straight month in June and a measure of prices paid by factories for inputs dropped to a six-month low amid weak demand for goods.

The two-year U.S. Treasury yield, which typically moves in step with interest rate expectations, rose 5.7 basis points to 4.777%, putting them at a high two-week high.

The selloff was a bear steepener, in which longer-duration Treasuries lost more ground than those with shorter durations, leaving the closely watched gap between yields on two- and 10-year Treasury notes, at a negative 30.1 basis points, its least inverted position since May.

Trading will close early Wednesday and the bond market will be closed Thursday due to the Fourth of July holiday. (Reporting by David Randall; editing by Jason Neely, Anil D'Silva and Alexander Smith)