* Draghi strengthens message on potential for more easing
* Euro falls to 5-week low vs dollar, 1-yr low vs sterling
* Analysts still warn thinner liquidity may push rates up
By Marius Zaharia and Patrick Graham
LONDON, Jan 9 (Reuters) - Euro zone money market rates fell and the euro currency weakened on Thursday after the head of the European Central Bank gave his clearest message yet about what could trigger further monetary easing.
President Mario Draghi laid down two triggers for further action, saying the ECB would try to fight further falls in inflation or an unwarranted rise in money market rates.
His more specific guidance on future moves came after euro zone inflation slowed to 0.8 percent in December, much lower than the ECB's target of nearly 2 percent, and as signs of a pick-up in growth and falling excess cash levels in the banking sector had begun to nudge short-term rates higher.
The ECB wants to avoid a rise in money market rates - rates at which banks lend to each other and which set the baseline for the cost of lending across the economy - as that would effectively tighten monetary conditions, limiting the potential for economic growth and pushing inflation even lower.
"This is bold talk from the ECB and suggests that the bank means business," said Kathleen Brooks, head of research at Forex.com. "The rose-tinted glasses have been thrown off and Draghi and co will not be moved from their dovish path even though there have been further signs that the currency bloc is turning a corner and returning to growth."
The euro hit a five-week low of $1.3548 and, against sterling, a one-year low of 82.30 pence in reaction to Draghi's comments.
The euro later recovered somewhat but many analysts say the divergence in policy outlooks between the world's major economies will weigh heavily on the single currency this year.
Money market rates implied by Euribor futures in 2014 and 2015 fell by up to 3 basis points, while German two-year bond yields dropped 2.6 bps to 0.21 percent, before rebounding slightly. German Bund yields, the benchmark for euro zone long-term borrowing costs, were little affected by Draghi's remarks.
His signals were likely to support this year's strong rally in lower-rated bonds as rock-bottom interest rates encourage investors to maximise their returns by buying riskier assets.
Portuguese bonds were standount performers. Ten-year yields fell 3 bps to 5.40 percent, as Lisbon drew solid demand for a 3.25 billion euro five-year bond sale on Thursday.
French yields rose as the national audit office said the country's debt level was in the "danger zone."
Draghi also tried to play down the relationship between money market rates and excess liquidity, which is money banks have beyond what they need for their day-by-day operations.
Analysts say the less liquidity in the system, the more likely that banks will need to borrow cash from other banks, putting upward pressure on money market rates.
The euro overnight lending rate rose to 0.137 percent on Wednesday from 0.099 percent the previous day as the excess liquidity dropped to 157.4 billion euros from 279 billion. The average Eonia rate for 2013 was 0.09 percent.
Forward Eonia rates for the next two years dropped a few basis points after Draghi's comments, though.
"He went out of his way (to talk down short-term rates)... I didn't find his arguments too convincing, but his dovish guidance would have helped to limit the damage on forward rates," Societe Generale strategist Ciaran O'Hagan said.
Banks this week took one-week loans of 112.5 billion euros from the ECB, while loans for 168.7 billion expired, draining 56.2 billion from the system. The ECB also absorbed the entire stock of 179 billion euros of its sovereign bond purchases, after failing to drain the whole sum at the end of 2013 when liquidity was thin, taking out a further 74 billion.
The ECB is holding weekly tenders to hoover up the cash injected into the system when it bought bonds at the height of the crisis, in an effort to ease concerns about direct state financing, something it is not allowed to do.
Excess cash is expected to drop further as repayments of the ECB's three-year crisis loans taken in late 2011 and early 2012 resume next week.
"It is something to watch," said ICAP strategist Philip Tyson. "If it falls (below) 100 billion and Eonia is ticking towards the ECB's refinancing rate (of 0.25 percent), this will increase speculation of (further easing)."