Anxiety over a possible Greek debt restructuring and an outlook warning on the United States spurred safety bids for U.S. Treasury bills and pushed their rates lower on Monday.

A Greek newspaper report -- later denied -- that Athens told the International Monetary Fund and the European Union that it wants to restructure its debt, fueled further stress in markets after last week's suggestion by Germany that it may support such a move.

Standard & Poor's further rattled investor confidence when it revised its long-term outlook on the United States to negative from stable due to its huge deficit and heavy indebtedness. This raised the risk the world's biggest economy could lose its coveted AAA-rating in two years, raising its borrowing costs.

It's a red-flag to our politicians to address our deficit issue, Larry Milstein, head of government and agency trading at R.W. Pressprich & Co. in New York, said of the S&P move.

While the path to achieve a deficit agreement will likely be rocky, there were thoughts that a long-term solution with a goal to pare the $14.3 trillion debt load over a dozen years is a long-term positive for the United States, said Michael Mata, portfolio manager who helps run the $520 million ING Global Bond Fund in Atlanta.

Still a deal between Obama and Republican leaders must be deemed credible, else the market will react negatively, Mata said.

U.S. Treasury bills fell 0.5 to 1.0 basis points on the day, as investors bailed out of stocks and other risky assets.

The one-month T-bill rate was quoted within striking distance from zero, a level touched in the beginning of April due to an insurance premium increase on bank assets from a U.S. agency.

In the new-issue market, bidding for T-bills surged.

At Monday's $30 billion auction of three-month bills, dealers and investors submitted $144.5 billion worth of bids, or a bid-to-cover ratio of 4.82, which was the highest since 4.95 at an auction on August 30.

In the meantime, the bid-to-cover ratio at the $28 billion six-month bill auction was 4.79, which was the highest since the auction held on November 1.

Interest rates futures also rose on a combination of safehaven bids and reduced expectations that central bankers will raise interest rates quickly due to fiscal predicaments in the U.S. and Europe, analysts said.

Eurodollar futures rose as much 11.5 ticks on the day, implying traders expected private dollar borrowing costs would decline.

On the other hand, Greek bond yields and credit default swaps hit fresh euro-era highs on Monday, dragging yields for other highly-indebted euro zone states higher.

We seem to have a continued deterioration in peripheral yields. This does put a little flight to quality (bid) into Eurodollars, said Alex Manzara, vice president at TJM Futures in Chicago.

(Additional reporting by Kirsten Donovan in London)

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