(Adds new comment, auction results, updates prices)

* Hormuz to stay closed, Iran says

* Investors brace for US CPI data on Wednesday

* Focus on US 3-year note auction, could see weak demand

* US yield curve flattens, but hits steepest since May

earlier

By Gertrude Chavez-Dreyfuss

NEW YORK, Aug 11 (Reuters) - U.S. Treasuries pared earlier

gains on Tuesday as initial optimism over a potential U.S.-Iran

agreement waned after an Iranian official said the Strait of

Hormuz would remain closed unless the United States met the

country's demands.

In afternoon trading, the benchmark 10-year yield slid less

than a basis point to 4.690%, while U.S. 30-year

bond yields were little changed at 5.241%. Yields

move inversely to prices.

On the shorter end of the curve, the yield on 2-year notes

, which are sensitive to market expectations for

Federal Reserve rate moves, slipped 1.7 bps to 4.222%.

Treasury's $58 billion auction of three-year notes was

absorbed smoothly on Tuesday, paring declines in yields on the

front end of the curve.

U.S. yields came off their lows after the newly appointed

secretary of Iran's Supreme National Security Council said the

strait will remain closed as long as the U.S. does not change

its behavior and accept Iran's conditions to end the war.

U.S. crude futures settled higher as a result, rising 1.3%

to $83.20 per barrel.

Iran's comments offset an earlier report from Bloomberg that the

United States and Iran were close to "some sort of an

arrangement," citing Pakistan's Defence Minister Khawaja Asif.

WAITING FOR CPI

Investors are also awaiting key inflation data - the U.S.

Consumer Price Index - due on Wednesday, which could determine

the path of interest rates.

"If you know where oil prices and CPI are going, you can

tell where Treasury yields are going as well," said Stan

Shipley, fixed income strategist at Evercore ISI in New York.

He noted, though, that long-term break-even inflation is

well contained, which means the market thinks the Federal

Reserve will get prices under control.

"Maybe we have some problems in the short term here over the

next year, but the long term over the next 10 years is fine. So

unless inflation blows out again, I don't think the 10-year is

going to go through this 4.70% hurdle."

Consumer prices are expected to edge up 0.1% in July after

falling 0.4% in June, according to a Reuters poll. Annual CPI

inflation is forecast to slow to 3.4% from 3.5% a month earlier.

Core CPI, which excludes volatile food and energy prices, is

also projected to rise 0.2% on the month, from an unchanged

reading in June, with annual core inflation seen easing to 2.5%

from 2.6% the previous month.

The headline U.S. Producer Price Index is expected to

increase 0.2% in July after declining 0.3% in June. On an annual

basis, PPI inflation is forecast to ease to 4.9% from 5.5% in

June. PPI data is due on Thursday.

SEPTEMBER RATE HIKE ODDS DIP

Going into the CPI data, U.S. rate futures priced in on

Tuesday a 48% chance of a hike at the Fed's policy meeting next

month, down from a 52.2% probability late on Monday. Traders are

also expecting just 29.7 basis points of tightening this year.

Tuesday's auction of three-year notes was well received,

with the debt pricing at 4.291%, below forecasts, indicating

investors did not demand a premium to absorb the supply.

The bid-to-cover ratio, a gauge of investor appetite, was

2.71 times, higher than the 2.61 average.

U.S. 3-year yields have risen around 11 bps since the last

auction and Jay Barry, head of global rates strategy at J.P.

Morgan, pointed out in a research note that the sector "appears

fairly valued after adjusting for the level of rates and the

shape of the curve over the last three to six months."

Following the 3-year note auction, three-year yields

declined 1.5 bps to 4.291%.

In other parts of the bond market, the yield curve was

little changed on Tuesday ahead of the CPI and PPI numbers, with

the gap between 2-year and 10-year yields at 46.4 bps

, compared with 46.2 bps late Monday.

Earlier in the session, the curve hit 47.6 bps, its steepest

level since May 22.

The curve showed a bull steepener, a scenario in which

short-term interest rates are falling a little faster than

longer-dated ones.