Eonia, the euro zone overnight bank-to-bank lending rate, has been volatile, spiking above the ECB's key rate at times, as banks repay their crisis loans with confidence returning and lenders shaping up for the ECB's balance sheet check this year.

The concerns were raised at a December meeting of the money market contact group (MMCG), which includes around 20 top traders and a handful of top ECB experts, and the ECB said in January it would act if such tightening became "unwarranted".

"A number of MMCG members were concerned that the 'normalisation' of the EONIA towards 25 basis points was too swift in view of the current state of market functioning and fragmentation," minutes of the December meeting showed.

"In their view, the tightening was driven by the pace of the ongoing repayments of the three-year longer-term refinancing operations, which exceeded the pace of the market normalisation and was partly attributed to banks' reluctance to participate in central bank operations," the report said.

One reason for such reluctance could be the end-of-the-year cut off date, which the ECB will use to assess the euro zone's top lenders' balance sheets, checking whether they have allocated sufficient capital to meet potential losses.

But bank funding issues, liquidity ratios and central bank funding will not be covered in the ECB's so-called asset quality review (AQR), the minutes also said.

ECB President Mario Draghi reiterated after the January policy meeting that it was very difficult to draw conclusions on the relationship between excess liquidity and Eonia, saying the ECB would watch developments closely and act if necessary.

Excess liquidity, or money banks have beyond what they need for their day-to-day operations, has fallen to 170 billion euros, down from a mid-2012 peak of 800 billion.

ECB governing council member Klaas Knot said at the weekend that the ECB was concerned about the volatility in short-term interest rates, but was not ready to engage in any policy action to counter it for now.

A possible response would be another cut of the ECB's main refinancing rate, but it is unclear whether the ECB would then also cut its deposit rate below the current level of zero, effectively charging banks to hold their cash overnight.

The negative deposit rate was also discussed at the MMCG December meeting, and a number of members "warned of a possible adverse impact on money market activity", the minutes showed.

"One member noted that it could improve market fragmentation across euro area countries," it said.

(click here for the full document: http://www.ecb.europa.eu/paym/groups/pdf/mmcg/20131210/summary.pdf?18eefe582928e2c3d4468bbd12828529)

(Reporting by Eva Taylor and Sakari Suoninen; Editing by Hugh Lawson)

By Eva Taylor