The three-month Euribor rate, traditionally the main gauge of unsecured bank-to-bank lending, rose to 0.223 percent from 0.220 percent.
Euribor rates have fallen by around 85 percent since late last year when the ECB started flooding money markets with cheap ultra long-term loans.
While markets expect another rate cut this year, the ECB is expected to keep its main refinancing rate at a record low of 0.75 percent this week as it wants to keep some weapons in its arsenal.
Six-month Euribor rates also rose, to 0.438 percent from 0.437 percent. One-week rates ticked up to 0.084 percent from 0.083 percent while Eonia overnight rates rose to 0.107 percent from 0.095 percent.
Dollar-priced three-month bank-to-bank Euribor lending rates increased to 0.639 percent from 0.635 percent, while overnight dollar rates remained at 0.322 percent.
The ECB's move to stop paying interest on banks' deposits has prompted banks to make stronger use of the current account facility, which still pays 0.75 percent interest for the required reserves.
A total of 316 billion euros was parked in the ECB's deposit facility overnight. Banks' current account deposits at the ECB fell to 526 billion euros.
Euribor rates are fixed daily by the Banking Federation of the European Union (FBE) shortly after 0900 GMT.