* Money markets still see slim chances of 25-basis-point Fed

hike on Wednesday

* 7-year bond auction coming up later in the day

* 10-year, 30-year Treasury yields at about one-week low

By Shashwat Chauhan

July 28 (Reuters) - U.S. Treasury yields fell to their

lowest levels in about a week on Tuesday, extending declines

into a third straight session as oil prices continued to fall on

rising hopes that the conflict between the United States and

Iran could see a resolution, heading into the Federal Reserve's

rate decision this week.

Oil prices slipped to a more than one-week low after topping

the $100 a barrel mark last week. U.S. President Donald Trump on

Monday said the United States was having "good talks" with Iran

and there was a chance of a deal over their conflict, but warned

that U.S. strikes would resume if the negotiations failed to

deliver.

Things remained shaky at best as Saudi Arabia, Jordan and

Iraq reported drone attacks on Monday. Brent crude futures

were last down 2.8% at $83.5 per barrel, still about 17%

above levels seen before the conflict began earlier this year.

"A return to pre-war and early July levels is a big ask

without fully-fledged commitment to peace and re-opening of the

Strait of Hormuz," Societe Generale strategists said in a note.

The yield on the benchmark U.S. 10-year Treasury note

shed 2.3 basis points to an about one-week low of

4.618%, down for the third straight session -- a streak last

seen a month ago.

Yields on the 30-year bond also dipped for the

third straight day, down 1.3 basis points at 5.112%.

Despite the recent declines, yields on 10-year and 30-year

bonds are set for their biggest monthly jump since March, as

traders ramp up interest-rate hike bets on growing inflation

concerns due to the oil spike. The 2-year yield is

headed for a fifth straight monthly rise.

EYES ON THE FED

While investors broadly expect the Fed to hold its main

lending rate steady on Wednesday, there is some scepticism.

Money markets show traders still see a near 34% chance of a

25-basis-point rate hike, according to the CME FedWatch Tool.

"This reflects renewed geopolitical tensions, the absence of

explicit guidance, and perhaps the fact there is a press

conference. Such elevated odds just two days before an FOMC

meeting are quite unusual, as the Powell-era Fed generally

telegraphed moves clearly," said Xiao Cui, senior economist at

Pictet Wealth Management.

Last month, Fed Chair Kevin Warsh, in his first meeting at

the helm of the central bank, moved quickly to trim the Fed's

public messaging, delivering a shortened policy statement and

explicitly declining to offer forward guidance in a return to a

format similar to that used by former Chair Alan Greenspan.

Traders are fully pricing in the chance of a September rate

hike, along with a 68% chance of an additional hike by year-end.

U.S. President Donald Trump on Monday called on the Fed to lower

interest rates.

Investors will watch the outcome of a 7-year Treasury

auction later in the day following a solid sale of 2-year debt

and a sale of 5-year paper that attracted softer demand on

Monday.

On the economic data front, the June U.S. Personal

Consumption Expenditures Price Index, which has typically been

the Fed's favoured measure of inflation, lands on Thursday,

along with a second-quarter GDP reading.

(Reporting by Shashwat Chauhan in Bengaluru; Editing by Amanda

Cooper and Mrigank Dhaniwala)