* Banks funding remains pressured despite Irish rescue
* ECB faces exit strategy dilemma this week * Eonia now seen above 1 percent in Nov. 2011
By Kirsten Donovan and Emelia Sithole-Matarise
LONDON, Nov 29 (Reuters) - Peripheral euro zone banks funding conditions remained pressured on Monday as a bailout package for Ireland failed to draw a line under debt concerns, leaving the ECB with a tricky decision to make later this week.
Irish government bond yields fell on Monday after the European Union approved an 85-billion-euro rescue for Ireland and outlined a permanent system to resolve Europe's debt crisis.
But elsewhere on the periphery, the news was received more cautiously with yields on Spanish 10-year debt rising as the moves did little to reduce expectations that Portugal -- whose banks are heavily reliant on European Central Bank (ECB) funding -- and possibly Spain, would also need financial assistance.
That leaves the ECB with a dilemma, as it has promised to tell markets this week whether or not it will continue to withdraw the extraordinary liquidity provision measures put in place during the financial crisis.
"There's a lot of evidence that the crisis is not over and that there are still a lot of banks remaining dependent on ECB liquidity and not only in Greece and Ireland but also in some stronger countries such as Germany," said Patrick Jacq, a strategist at BNP Paribas.
Jacq and other strategists expect the liquidity-sensitive Eonia EONIA= overnight rate to fall as low as 0.37 percent by the end of the current ECB reserve maintenance period next week, after rising as high as 0.80 percent around Nov. 10 when the maintenance period began. The overnight rate traditionally sits above the ECB's refinancing rate. Eonia EONIA= fixed at 0.446 percent on Friday.
Forward markets were now showing overnight EONIA rates rising above the ECB's key refi rate currently at 1 percent by November compared with July last week.
"It is looking increasingly possible that the (ECB) Governing Council might elect to postpone a decision on further exit measures until the first quarter of 2011," Barclays Capital strategists said in a note.
"There would not be much cost in agreeing to a postponement, in order to avoid possible inflammation of the currently prevailing market stress.
Until market stress intensified last week, the prevailing market view was that the ECB would switch its tenders of 3-month money back to a variable rate, limiting the amount on offer, albeit possibly to much more than banks actually need.
The escalation of euro zone tensions has pushed the cost of raising funds in secured lending markets higher in recent weeks.
The five-year euro/dollar cross-currency basis swap EURCBS5Y=ICAP, which shows the rate charged when swapping euro interest payments on an underlying asset into dollars, fell to -36 basis points on Friday, near the -39 bps reached in May when Greece had to take funding from the International Monetary Fund and EU indicating a reluctance to swap dollars for euros.
It was last at around -36.5 bps, showing little relief after the weekend's events.
Some pressure on banks eased however, after the EU opposed making senior bank bondholders share the bailout burden by taking write-downs.
The cost of insuring senior financial debt against default, as measured by the iTraxx senior financials index ITEFA5Y= pared early tightening to stand 2.5 bps lower on the day at 162 bps, according to data monitor Markit.
"This will provide relief to the markets, and should also give support to paper of Portuguese and Spanish banks," BNP Paribas credit strategists said.
Benchmark three-month euro Libor rates EUR3MFSR= slipped to 0.96750 percent from 0.96875 percent with equivalent dollar rates USD3MFSR= barely changed at 0.29594 percent. For latest Libor fixings see [ID:nEAP000020] (Editing by Susan Fenton)