* Eonia contracts fall, curve flattens after ECB conference
* ECB President Draghi seen calming fears of liquidity drain
* Euro slides vs dollar as traders unwind recent steepening
LONDON, Feb 7 (Reuters) - Longer-term money market rates eased on Thursday after European Central Bank President Mario Draghi sought to temper the rise in interbank borrowing costs since banks began paying back three-year ECB loans early.
Draghi estimated that, even after the initial repayments of the second of the ECB's LTRO crisis loans, excess liquidity would not drop below 200 billion euros ($268 billion) - the level at which overnight borrowing costs typically begin to rise.
He also said the central bank would closely monitor conditions in the money market and their impact on monetary policy, stressing that the ECB would remain "accommodative".
That double-barrelled warning against ramping up market rates to an extent that effectively tightens monetary conditions prompted some interbank borrowing rates to fall.
"I would base this move mainly on their liquidity expectations, and the signal that, if their liquidity estimations prove wrong at some point, the ECB would fall back on this other option of 'closely monitoring'," said Benjamin Schroeder, strategist at Commerzbank.
One-year Eonia contracts fell 3 basis points to 0.16 percent while the two-year rate dropped 5 bps to 0.27 percent - a flattening of the money market curve that partially unwound the recent trend.
Since the first repayment of ECB loans came in well above consensus last month, money market curves have steepened as traders brought forward the timing of when surplus cash in the system would fall low enough to push rates up.
The next major batch of repayments will come on Feb. 22 when banks have their first opportunity to pay back some of the 529 billion euros borrowed at the ECB's second refinancing operation in March last year.
A Reuters poll on Monday showed traders expect 123 billion to be paid back in that tranche. That would not be enough to take the excess liquidity pumped in by the ECB below the 200 billion euro threshold. Reuters data shows the current liquidity excess at 495 billion euros.
Market participants also highlighted the central bank's increased emphasis on the appreciation of the euro, which hit a 15-month high last week spurred in large part by the rise in short-term euro market interest rates.
But the euro fell versus the U.S. dollar during the news conference, putting in on course for its biggest daily fall since June, as Draghi said the exchange rate was important to growth and price stability.
Analysts said this fall reflected the flattening in money market curves.
"Draghi struck an optimistic tone, but was maybe slightly more concerned about the LTRO repayments and euro strength than most had expected. Thus short rates are falling a bit and the euro is weakening slightly," said Nordea chief analyst Anders Svendsen in a note.