Updated in New York afternoon time

By Karen Brettell

NEW YORK, March 10 (Reuters) - U.S. Treasury yields were mixed on Tuesday, edging up from their early lows after a media report that U.S. intelligence detected signs Iran may be considering steps to deploy mines in the Strait of Hormuz.

The report, in a post on X by CBS News, added to lingering concerns that a prolonged conflict in the Middle East could weigh on global oil supplies and fuel inflation. President Donald Trump later said the U.S. had no reports of Iran placing mines, and warned of military consequences if mines were placed and not removed.

Yields had dropped earlier in the session after Trump said the U.S.-Israeli war on Iran could soon be over.

Adding to uncertainty, the White House said the U.S. military had not yet escorted any commercial ships through the Strait of Hormuz, just after Energy Secretary Chris Wright deleted a social media post that said the U.S. Navy had escorted an oil tanker through the key waterway.

Yields have been volatile over the past week or so, rising on concerns that higher oil prices could push up inflation and prompt the Federal Reserve to delay cutting interest rates.

"You probably can't get Fed rate cuts in an environment when there are commodity shortages and price spikes," said John Luke Tyner, head of fixed income and portfolio manager at Aptus Capital Advisors in Fairhope, Alabama.

"We're seeing some cuts being pushed out and an inflation premium tick into the long end of the curve," he said.

Fed funds futures traders are now pricing in 41 basis points of cuts by year-end, indicating doubts over whether the U.S. central bank will make a second 25-basis point cut this year.

The yield on benchmark U.S. 10-year notes US10YT=RR was last up 0.4 basis points on the day at 4.138%. The two-year note US2YT=RR yield fell 2.1 basis points to 3.571%.

The yield curve between two- and 10-year notes US2US10=TWEB steepened by around half a basis point to 56 basis points.

Consumer price inflation data for February due on Wednesday will be a key economic focus this week. It is expected to show that core consumer prices rose by 0.2% during the month while headline prices rose by 0.3%, according to the median estimate of economists polled by Reuters.

Investors will likely be more worried about an upside surprise, said Will Compernolle, macro strategist at FHN Financial, in part because Personal Consumption Expenditures data on Friday is expected to show a higher increase.

Friday's PCE report for January is expected to show a 0.3% increase in headline inflation during the month, and a 0.4% increase in core prices.

"Economic data has the potential to regain some of its relevancy after oil prices fell yesterday and two-year Treasury yields are now only about 10 bp above levels that prevailed in late February," economists at Citi, led by Andrew Hollenhorst, said in a report on Tuesday.

The bank expects the CPI data to show a monthly increase of 0.23% in core inflation, "much softer than last year's February reading and consistent with the idea that core inflation is slowing."

"Higher oil prices imply higher headline inflation but pass-through to core would be limited if the rise in oil prices proves to be short-lived," Citi said.

Data on Tuesday showed that U.S. existing home sales unexpectedly increased in February as lower mortgage rates and a moderation in house-price growth pulled buyers back into the market.

The Treasury saw soft demand for a $58 billion sale of three-year notes on Tuesday, the first auction of $119 billion in coupon-bearing supply this week.

The notes sold at a high yield of 3.579%, more than a basis point above where they traded before the sale. Demand was 2.55 times the amount of debt on offer, the lowest since August.

The Treasury will also sell $39 billion in 10-year notes on Wednesday and $22 billion in 30-year bonds on Thursday.