TREASURIES-Two-year yields dip as Hormuz flows rise, hopes on inflation grow

* Fed funds futures traders price 63% odds of a rate hike by September

* Nine of 18 Fed policymakers projected at least one 2026 rate increase

* Reuters-polled economists expect June payrolls growth of 110,000 jobs

By Karen Brettell

NEW YORK, June 26 (Reuters) - Short-dated U.S. Treasury yields fell on Friday, tracking lower oil prices, after crude shipments through the Strait of Hormuz rose to their highest level since the U.S.-Israeli war against Iran began, fueling hopes that the worst of the recent inflation shock may be passing.

Optimism is growing that easing energy prices, as the peace agreement takes hold, will feed through to lower inflation in coming months - even as price pressures continue to run well above the Federal Reserve's 2% annual target. Traders are also weighing the odds of a Fed rate hike after nine of the 18 policymakers who submitted projections in the "dot plot" at the June meeting indicated they expect at least one rate increase in 2026.

"I think a lot of those hawkish dots were from non-voting regional presidents," said Will Compernolle, macro strategist at FHN Financial. "The center of gravity is still - let's just stay on hold for now. The bar for hiking is a lot higher than markets expect."

New Fed Chair Kevin Warsh also did not provide a rate outlook in line with his preference for less forward guidance.

Fed funds futures traders are pricing in 63% odds of a rate hike by September.

The 2-year note yield, which typically moves in step with Fed interest rate expectations, fell 2.68 basis points to 4.094%, the lowest since June 17.

The yield on benchmark U.S. 10-year notes rose 0.41 basis points to 4.396%.

The yield curve between 2- and 10-year notes steepened to 30 basis points.

While Fed officials remain focused on inflation, the labor market is a wild card that could shift policy expectations if it were to materially weaken. Three stronger-than-expected monthly jobs reports have bolstered the case for tighter monetary policy.

"I don't think anyone is worried about the labor market right now, so if next week's data shows some sort of weakness I don't think it's enough to totally change the story, but suddenly labor market risks could come back onto the radar," said Compernolle.

The jobs report for June is due on July 2 and is expected to show that employers added 110,000 jobs during the month, according to the median estimate of economists polled by Reuters.

(Reporting by Karen Brettell; Editing by Andrea Ricci )