* US bill rates pushed down by Fed stimulus program
* Three-month Euribor rate rises for first time in 3 months
* European money markets give up on the idea of deposit rate cut
(Adds strategist's comments, changes dateline from previous LONDON)
By Chris Reese and Marius Zaharia
NEW YORK/LONDON, Oct 1 (Reuters) - The U.S. Treasury on Monday sold $32 billion of three-month bills at the lowest interest rate since June, as a Federal Reserve stimulus program put some downward pressure on shorter-dated rates.
The Treasury sold the three-month bills at a high rate of 0.085 percent, down from a high rate of 0.11 percent at a similar sale last week and the lowest since a three-month bill sale on June 11.
One of the Fed's stimulus program, nicknamed "Operation Twist" because the central bank is selling shorter-dated Treasuries to buy longer-dated Treasuries, was seen as dragging on shorter-dated rates.
"Data on primary dealer bond positions show that their holdings of Treasuries have climbed since the start of Operation Twist last October," said Alex Roever, short-term rates strategist at J.P. Morgan Securities in New York, adding "of that increase, 75 percent were concentrated in coupons maturing in three years or less."
"With the Fed extending Operation Twist to the end of this year, dealers continue to be cluttered with short Treasuries," Roever said.
A Treasury auction of $28 billion of six-month bills on Monday brought a high rate of 0.135 percent, down from a high rate of 0.14 percent in a similar sale last week but up from a high rate of 0.13 percent in an auction two weeks ago.
Meanwhile in Europe, key Euribor interbank lending rates rose on Monday for the first time in three months as expectations that the European Central Bank could cut interest rates this week are fading.
Money markets are also in the process of pricing out the possibility that the deposit facility rate will ever be cut into negative territory from the current zero percent.
Only a minor chance of such a move is factored in for the start of next year, but some banks are recommending clients to exit such bets or position for a rise in January-dated rates.
Economists polled by Reuters expect the ECB to leave its main refinancing rate flat at 0.75 percent at its meeting on Thursday.
The three-month Euribor rate
, traditionally the main gauge of unsecured bank-to-bank lending, rose to 0.223 percent from 0.220 percent.
"This points to more uncertainty creeping into the market with regards to any future rate cuts," said Elwin de Groot, senior market economist at Rabobank in Utrecht, the Netherlands.
"Rates are very low already and there's basically only one thing that could push down money market rates even further, and that would be a cut in the deposit rate. But that seems not to be a subject of discussion within the ECB."
ECB Executive Board Member Benoit Coeure said last week that a cut in the deposit rate, a move that would effectively charge banks to hold money with the ECB overnight, may not be beneficial for all segments of the market.
Imposing a penalty for parking cash at the central bank could shake things up in the dormant euro zone money markets and sway banks to take the risk of lending to each other more to get a return on their cash.
Healing money market segments that have been frozen by the euro zone debt crisis is seen as an important step towards restoring sustainable economic growth in the region.
However, the low level of short-term rates is already making some asset managers take cash out of money markets and put it in other assets such as bonds.
The forward Eonia market, showing where investors expect the overnight Eonia rate to be at certain points in the future, is completely dismissing the probability of a deposit rate cut in October.
The Eonia rate dated for the October meeting last traded at 0.09 percent. Eonia has fixed at an average of around 8 basis points over the deposit rate in the past few months.
(Editing by Neil Stempleman)
Keywords: MARKETS MONEY/