By Gertrude Chavez-Dreyfuss

NEW YORK, July 7 (Reuters) - U.S. Treasuries fell on Tuesday as investors monitored geopolitical tensions after attacks in and around the Strait of Hormuz drove oil prices higher, while bracing for a heavy slate of auctions expected to gauge appetite for U.S. government debt.

The benchmark 10-year yield, which moves inversely to Treasury prices, rose to a four-week peak of 4.521% US10YT=RR and was last up 2.8 basis points (bps) at 4.507%. U.S. 30-year yields also hit a four-week high and last changed hands at 5.023% US30YT=RR.

U.S. yields advanced in the wake of reports that Iran fired missiles at ships in the critical Hormuz waterway, analysts said, lifting oil prices and endangering a key peace memorandum of understanding between the United States and Iran.

U.S. crude futures were 2.3% higher on Tuesday at $70.13 per barrel CLc1. Elevated energy costs threaten to keep inflationary pressures alive, potentially delaying the Federal Reserve's push to bring inflation back to target if peace talks break down.

Stan Shipley, fixed-income strategist at Evercore in New York, said Iran's action "changes the mood in the Treasury market," with yields grinding higher in response to an increase in oil prices.

On the front end of the curve, U.S. 2-year yields, which reflect interest rate expectations, edged higher by 1.2 bps to 4.137% US2YT=RR and rose after two days of declines.

The yield curve steepened for a fifth consecutive session, with the gap between 2-year and 10-year yields widening to as much as 37.6 bps US2US10=TWEB. That's the highest gap in three weeks. The curve was last at 37.2 bps, compared with 35.5 bps late on Thursday.

The curve showed a bear steepening move, where longer-dated yields are rising more sharply than those on short-term maturities, reflecting a reduction in rate hike bets from the Federal Reserve.

U.S. rate futures on Tuesday priced in a 66.4% chance of a rate increase by the late October policy meeting at the Fed, down from about 75% a week ago, according to the CME's FedWatch.

HEAVY SUPPLY

The market is also looking to heavy Treasury supply this week. Ahead of bill and note auctions, investors often sell Treasuries to push yields higher before buying them back at lower prices once new supply is absorbed — a process known in the market as building a concession.

On tap on Tuesday are $142 billion in U.S. six-week and 52-week bill auctions and the sale of $58 billion in three-year notes. The Treasury will also auction 10-year notes on Wednesday and 30-year bonds on Thursday.

Ahead of the auction, U.S. 3-year yields climbed 2.6 bps to 4.163% US3YT=RR.

Vail Hartman, U.S. rates strategist at BMO Capital in New York wrote in a research note demand for U.S. Treasuries in the last few months has been generally weak, noting that only 28% of coupon auctions have come in within or above expectations. He expects the same outcome for the U.S. three-year note auction later on Tuesday.

"The pullback in aggressive auction bidding in recent months can be attributed to heightened macroeconomic uncertainty, elevated headline risk, and volatile intraday price action," Hartman said. "We suspect that these factors will continue to temper demand for the 3-year sector."

Evercore's Shipley, however, believes this week's Treasury supply will be well-subscribed, including Tuesday's sale of U.S. 3-year notes.

"Just talking to clients, they want to be in Treasuries," he said. "They know the risk out there is more elevated, so they're not really going short."