(Updates prices, auction results, adds analyst quotes)

* Fed is widely expected to keep interest rates steady

* US Import Price Index rose 1.9% in May

* Auction of $13 billion 20-year notes had good demand

By Tatiana Bautzer

NEW YORK, June 16 (Reuters) - Yields on U.S. Treasuries fell

on Tuesday, as oil prices reached a three-month low with

optimism about the deal between the U.S. and Iran and investors

waited for Wednesday's Fed meeting.

The 10-year Treasury note was last down 4.5

basis points at 4.424%. The $13 billion, 20-year note auction

was successful, and 20-year yields that peaked at 4.938% during

the trading day were at 4.93%.

The Fed is widely expected to keep interest rates steady on

Wednesday, and to remove its reference to an easing bias.

Markets will focus on the language in its policy statement, the

release of updated policymaker projections and what Kevin Warsh,

an appointee of President Donald Trump who took over from former

Fed chief Jerome Powell last month, says in his post-meeting

press conference.

The two-year U.S. Treasury yield, which

typically moves in step with interest rate expectations for the

Fed, fell 1.7 basis points to 4.047%.

Analysts believe that even if the Strait of Hormuz is

reopened in the short term and the price of oil drops to pre-war

levels, it would not likely be enough to contain widespread

inflation pressures.

U.S. import prices rose 1.9% in May, above the 1% forecast by

economists in a Reuters poll. The index was up 6.7% on a

year-over-year basis, the largest rise since August 2022. BMO

analysts said in a report on Tuesday that the rise in import

prices should add to upward pressure on the Personal Consumption

Expenditures Price Index excluding food and energy items in May.

"Inflation pressures have broadened beyond the pass-through

of oil prices," said Guneet Dhingra, head of U.S. Rates Strategy

at BNP Paribas. "Even if the oil falls to pre-war levels, we do

not expect interest rates to follow."

There were also renewed signs of some weakness in the U.S.

housing market, with housing starts plummeting 15.4% in May, the

largest decline since March 2024.

Markets will be focused on what Warsh will say in the press

conference and how the communication will change. Warsh has

publicly said he believes the Fed should not give forward

guidance.

"That has the potential to create volatility," Dhingra said.

BNP expects the Fed to begin tightening rates by the end of

the year, and its analysts believe the neutral interest rate now

is higher. The 10-year TIPS breakeven rate, which subtracts the

TIPS yield from the nominal Treasury yield and is viewed as a

proxy for inflation expectations, was last at 2.299%, indicating

the market sees inflation averaging about 2.3% a year for the

next decade.