Bank-to-bank dollar funding costs fell on Tuesday with the benchmark rate hitting yet another record low as central banks signalled they were in no hurry to unwind extraordinary stimulus measures.

On Monday, U.S. Federal Reserve Chairman Ben Bernanke reiterated the Fed's vow to keep interest rates exceptionally low for an extended period, saying tight credit and a weak job market would weigh on the economy's recovery.

Sounding a more optimistic note, however, Federal Reserve Bank of San Francisco President Janet Yellen said on Tuesday the U.S. economy will grow next year and accommodative policies cannot be maintained for too long. 

In the euro zone, European Central Bank President Jean-Claude Trichet repeated earlier comments that key interest rates were appropriate at the moment.

The three-month dollar London interbank offered rate USD3MFSR= was fixed near 27 basis points for the first time, while the equivalent rate for euros was set at 0.67375 percent, not far off the trough of 0.66938 percent plumbed in October.

The euro zone money market will get another injection of one-year funds from the ECB next month, which will add more long-term liquidity into a market already flushed with cash.

But central banks have urged financial institutions to be reasonable in bidding for funds at the next 12-month lending operation.

I don't think demand at the one-year tender will be as strong as the one in June (when the ECB allotted nearly half a trillion euros), said Patrick Jacq, strategist at BNP Paribas in Paris, adding he believed the December one-year tender will be the last one.

The ECB has said it'll not be able to maintain all the measures, this means some will remain and if they stop the one-year tender, I'm pretty sure they'll continue to offer cheap liquidity for three months and six months, he added.

KBC analysts said the end of the 1-year long term refinancing operation (LTRO) after the December tender looked a done deal.

Points of discussion remain the introduction of a spread over the main policy rate for the December 1-year LTRO and a potential reduction in the pace of other LTROs (3-6 month) in H1 of 2010, they said in a note.

Some banks have started to wean themselves off the ECB's cheap money. EFG Eurobank (EFGr.AT), Greece's second-largest lender, said on Tuesday it has halved its reliance on ECB funding as its cash position recovers from the worst of the credit crisis.

Meanwhile, Bank of England policymaker Andrew Sentance said Britain's economy was moving towards recovery and the central bank's latest forecasts showed the risk of keeping monetary policy too loose for too long.

Over the months ahead the BoE's Monetary Policy Committee would need to assess whether the signs of recovery were sufficiently well-established to remove the need for further stimulus from additional money injections, he said.