* Oil prices tumble around 4% to three-week low

* Fed funds futures price 59% odds of September rate hike,

down from 68% on Monday

* Two-year yield hits lowest level since July 21 as rate

expectations ease

By Karen Brettell

NEW YORK, Aug 4 (Reuters) - U.S. Treasury yields fell on

Tuesday as oil prices tumbled on hopes for a deal to end the

Iran war, leading traders to reprice for lower odds of a Federal

Reserve interest rate hike in September.

Oil prices were down around 4% to a three-week low. Qatar said

on Tuesday that mediators were making progress in efforts to end

the U.S.-Iran conflict. Adding to the optimism, Treasury

Secretary Scott Bessent said a deal on reopening the Strait of

Hormuz could be reached as early as Tuesday or Wednesday.

The developments boosted hopes that a resolution to the war

is near, though many investors remain cautious given several

false starts in negotiations so far.

"It's like Groundhog Day," said Lou Brien, market strategist

at DRW Trading.

"I don't think that (U.S. President Donald) Trump wants the

war going on when the (midterm) election is here. I don't think

any of the other countries around there really want the war

going on any further. They want to just find some status quo and

then just exist with it."

The 2-year note yield, which typically moves in

step with Fed interest rate expectations, fell 6.22 basis points

to 4.194%, the lowest level since July 21.

The yield on benchmark U.S. 10-year notes fell

4.91 basis points to 4.635%.

The yield curve between 2- and 10-year Treasury yields

was at 44 basis points.

The recent spike in oil prices amid the escalating war in

the Middle East had fueled speculation that the Fed might need

to raise rates to keep inflation in check, as price growth

remains stubbornly above the central bank's 2% target.

Traders are also still parsing comments last week from Fed

Chairman Kevin Warsh, who noted inflation risks but stopped

short of laying out a concrete plan to address them.

Fed funds futures are now pricing in 59% odds of a hike at the

Fed's September 15-16 meeting, down from 68% on Monday.

The Treasury Department is set to unveil details of its

funding plans for the coming two quarters on Wednesday, with

investors watching closely for any signals of increased issuance

of longer-dated debt.

The government said on Monday it expects to borrow $739 billion

in the third quarter, $68 billion more than projected in May,

and will release detailed auction sizes on Wednesday.