* Euro rates mark new lows as ECB holds rates
* Banks continue to hoard 1-yr funds
* EONIA at new low, traded overnight rates fall further
(Adds ECB rate decision, Libor fixings)
By Kirsten Donovan
LONDON, July 2 (Reuters) - The interbank cost of borrowing euros marked a new low on Thursday as the European Central Bank held rates and markets waited for clues on what it might do next to spur banks to start lending.
Overnight rates also hit new lows as the market continued to hoard the near half-trillion euros of 1-year funds the central bank doled out last week, with much of it making its way straight back to the ECB's vaults.
Overnight deposits at the ECB rose to a new 5-1/2 month high on Wednesday with banks depositing over 257 billion euros, the highest since mid-January, and above the 252 billion deposited on Tuesday [ID:nFAT004763].
BNP Paribas rate strategist Alessandro Tentori noted that compares with an average of 19 billion in the month before the tender, saying some members of the bank's Governing Council may not be comfortable with the excess liquidity given the aim of the tender was to encourage banks to resume longer-term lending.
"What can (the ECB) do? Either remove the excess, a contradiction with the fixed rate tender policy, or cut the deposit rate to zero in order to make recourse (to the deposit facility) more expensive," Tentori said.
"Most likely is they won't do anything this time, keeping the market in huge excess."
The ECB kept its main refinancing rate on hold at 1 percent as expected on Thursday.
Bank President Jean-Claude Trichet holds a news conference at 1230 GMT and could present the tender as proof the bank is committed to fighting recession, despite keeping interest rates higher than many of its peers in other parts of the world.
It could also take the opportunity to urge commercial banks once again to lend the funds on to the real economy. [ID:nLU618923]
The ample amounts of money currently sloshing around have pushed down overnight rates to record lows, barely above the ECB's deposit rate.
EONIA EONIA= rates fixed at 0.34 percent on Wednesday and traded rates have fallen even lower, with traders reporting rates as low 0.2 percent.
Commerzbank/Dresdner Kleinwort strategists said they believed the ECB would tolerate this situation, for the time being at least.
"We assume that the ECB will not imply that it is going to correct the very ample liquidity situation in the money market following the 12-month tender," they said in a note.
"It will tolerate the fact that the overnight rate has again come very close to the deposit facility rate and thus is undershooting the refi rate of 1 percent, or even present it as desirable."
The ECB has scheduled two further 12-month tenders later in the year, which could either be offered at the prevailing refinancing rate, currently 1 percent, or at a spread over that if the central bank wants to discourage banks from taking on more liquidity.
"We've looked for guidance on the overnight rate and Eonia before (from the ECB) and not got it," said Calyon rate strategist Peter Chatwell.
"It feels like there is a lack of understanding over their objectives as regards the really short rates...just a simple comment that they are happy with the current level of EONIA would really help us in money markets."
Traders also noted new lenders up to the 3-month maturity coming back into money markets now the half-year end has passed
Three-month euro Libor rates EUR3MFSR= shaved off another basis point to fix at 1.0600 percent, while equivalent dollar rates USD3MFSR= also marked a new low at 0.5775 percent.
For full details of Thursday's Libor fixings see [ID:nL2676932]
Meanwhile, with U.S. and European banks still reticent to lend, investors withdrew heavily from low-risk money market funds in the latest week.
U.S. money market assets tumbled by $46.5 billion in the week ended Tuesday to $3.6 trillion after a $15 billion increase in the prior week, the Money Fund Report said on Wednesday. [ID:nN01495369]. (Editing by Toby Chopra and Chris Pizzey)