Euro zone banks took 115.6 billion euros at the European Central Bank's weekly refinancing operation, about 600 million euros less than in the previous week. Banks will receive the cash on Wednesday.

At the same time, the ECB failed for the second week in a row to offset its earlier government bond purchases, draining 151.2 billion euros from the market instead of the intended 177.5 billion euros, the amount of bonds bought under the Securities Markets Programme it still holds.

Put together, the two operations resulted in the ECB's liquidity provisions remaining virtually unchanged, which is seen keeping a lid on overnight EONIA rates.

"I expect EONIA to remain below 20 basis points for the next week, with a possible rise to 23-25 basis points for the weekend," a euro zone money market trader said.

Friday is the last trading day of the month, which usually sees a rise in overnight rates as banks balance their books.

Short-term interbank rates have climbed in recent weeks due to falling excess liquidity - money banks have beyond what they need for their day-to-day operations - and have reached levels where they are putting pressure on the ECB to stop the rise.

A gradual rise in the rates is seen as a reflection of banks' efforts to wean themselves off central bank funding and return to tapping markets, a kind of normalisation, but if the increase accelerates it could threaten the euro zone's recovery.

The high level in excess liquidity means that banks do not have to scramble to borrow from each other and keeps downward pressure on market rates.

When excess liquidity fell to around 130 billion euros earlier this month, the overnight rate traded for four consecutive sessions above the ECB's refinancing rate - the first time since 2011 that this has happened.

Since then, it has fallen back below the 0.25 percent refi rate and fixed at 0.188 percent on Monday, as excess liquidity rose back to 170 billion euros.

The failure to fully offset the bond purchases had happened several times late last year, and is seen continuing as excess liquidity drops. Traders said the ECB would not lose sleep over the failures.

"I don't think they have a problem with it. Instead of the EONIA spiking, it stays at an acceptable level," the trader said. "There is not enough excess liquidity in the market for it to succeed."

It can still increase if banks stock up at an offer of three-month funds on Wednesday. Only 1.9 billion euros of funds are due to mature from the previous operation.

With the ECB providing banks with all the liquidity they request since the beginning of the financial crisis, overnight rates have usually traded just above the ECB's deposit rate. That rate is currently at zero.

But with money markets functioning better, rates have inched up recently as banks have cut down on extra funds they have held in case markets clog up again.

The ECB said in its January monthly report that volatility in short-term market rates would increase as excess liquidity wanes, making interpreting money-market rates more complex.

The euro zone's central bank pledged earlier this month to act should the rise in bank-to-bank lending rates that underpin borrowing costs across the economy become "unwarranted".

But ECB Governing Council member Klaas Knot was quoted as saying that the development did not require policy action yet, adding that forward rates had remained relatively stable.

One-year one-year forward rates - the most traded money-market instrument, which shows where one-year Eonia contracts are expected to be in a year - rose to 0.315 percent at the end of last year but have since fallen. They currently trade at 0.227 percent.

(Reporting by Sakari Suoninen; Editing by Catherine Evans)