MONEY MARKETS-US 4-week bill rates rise as dealers long on supply

* U.S. sells 4-week bills at highest interest rate in 4 weeks

* Frozen euro zone money markets see tentative thawing

(Adds strategist's quote, changes dateline, previous LONDON)

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NEW YORK/LONDON, Oct 2 (Reuters) - The U.S. Treasury sold four-week bills at the highest interest rate in four weeks on Tuesday as a Federal Reserve stimulus program, nicknamed "Operation Twist," kept dealers flush with shorter-dated debt.

Treasury sold $40 billion of four-week bills at a high rate of 0.1 percent, up from 0.055 percent in a similar sale last week and the highest since a four-week bill auction on Sept. 5.

Demand for the bills was diminished as dealers remain long shorter-dated debt while the Fed sells its shorter-dated securities and buys longer-dated Treasuries in an effort to lower longer-term borrowing costs like those on mortgages.

"Dealer balance sheets are still loaded to the gills with front-end U.S. Treasuries from Operation Twist sales," said Natan Magid, short-term markets strategist at RBS Securities in Stamford, Connecticut.

The bid-to-cover ratio in the sale - a measure of demand - was 3.86, the lowest since May 2011.

Meanwhile, euro zone money markets have shown tentative signs of recovery in recent weeks along with improving appetite for risk in the region, but even the optimists say the crisis will have to be past before interbank lending is back to normal.

Some analysts say a pick-up in volumes in overnight lending,

a fall in the amount banks borrow from the European Central Bank and debt issuance by Spanish banks are indicative of a thawing of money markets, but traders say the interbank markets remain frozen.

A sharp narrowing of the gap between three-month interbank lending rates and overnight rates to pre-U.S. crisis levels further shows the start of some return to normality, they say.

"(The spread) is trading at very tight levels. That is the best indicator that the stress in the interbank market is coming down," Alessandro Giansanti, rates strategist at ING in Amsterdam, said.

The difference between three-month Euribor

and overnight Eonia rates

- a key measure of counterparty risk - last week fell to 11 basis points, its lowest since mid-2007, and was trading around that level on Tuesday.

Appetite for riskier assets has increased since late July when ECB President Mario Draghi first hinted at a plan to buy sovereign bonds, saying the central bank would do what was necessary to preserve the euro.

The change in sentiment as well as technical factors have helped to narrow the Euribor/OIS spread.

The deposit rate - which serves as a floor to the overnight lending rate - was cut to zero on July 5. Euribor rates have continued to trend down since then on expectations of further monetary easing.

Traders say, however, that the reduction in funding risk has so far not translated into greater lending between banks.

(Editing by James Dalgleish)

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